THIRD AMENDED AND RESTATED REGISTRATION RIGHTS AGREEMENT

Exhibit 4.2

THIRD AMENDED AND RESTATED

REGISTRATION RIGHTS AGREEMENT

THIS THIRD AMENDED AND RESTATED REGISTRATION RIGHTS AGREEMENT (this “Agreement”) is dated as of May 15, 2007, and is made by and among Amedica Corporation, a Delaware corporation (the “Company”), the holders of certain securities of the Company who acquired such securities prior to the date hereof and whose names are set forth on Schedule A to be attached hereto (collectively, the “Prior Investors”).

RECITALS

WHEREAS, certain of the Prior Investors acquired shares of one or more of the Company’s Series A Convertible Preferred Stock, par value $0.01 per share (“Series A Preferred Stock”), Series B Convertible Preferred Stock, par value $0.01 per share (“Series B Preferred Stock”), Series C Convertible Preferred Stock, par value $0.01 per share (“Series C Preferred Stock”), and/or Series D Convertible Preferred Stock, par value $0.01 per share (“Series D Preferred Stock”), either originally issued pursuant to one or more respective subscription agreements entered into between the Company and each such Prior Investor in connection with the Company’s offerings of shares of Series A Preferred Stock, Series B Preferred Stock, Series C Preferred Stock and Series D Preferred Stock, or as a result of becoming a transferee of a Prior Investor; and

WHEREAS, certain of the Prior Investors received warrants (collectively, the “Warrants”) exercisable for shares of Series A Preferred Stock, Series B Preferred Stock, Series C Preferred Stock or Series D Preferred Stock (and exercisable for shares of Common Stock, as defined below, after an IPO, as defined below), either originally issued pursuant to one or more Warrant Agreements between the Company and such Prior Investors, or as a result of becoming transferees of Prior Investors who received such Warrants in connection with the Company’s offerings of shares of Series A Preferred Stock, Series B Preferred Stock, Series C Preferred Stock and/or Series D Preferred Stock; and

WHEREAS, the Prior Investors have registration rights pursuant to that certain Second Amended and Restated Registration Rights Agreement dated as of April 17, 2007 (the “Prior Registration Rights Agreement”), by and among the Company and the Prior Investors, or as permitted assignees of such registration rights pursuant to the terms of the Prior Registration Rights Agreement; and

WHEREAS, Section 17 of the Prior Registration Rights Agreement provides that it may be amended with the written consent of the Company and Investor Securityholders (as defined in the Prior Registration Rights Agreement) holding a majority of the then outstanding Registrable Securities (as defined in the Prior Registration Rights Agreement), and that any such amendment shall be binding on all parties to the Prior Registration Rights Agreement regardless of whether any such party has consented thereto; and

WHEREAS, the Company and Investor Securityholders holding a majority of the Registrable Securities outstanding as of the date hereof have resolved to amend and restate the Prior Registration Rights Agreement, and the Company and such Investor Securityholders have executed and delivered this Agreement;

NOW, THEREFORE, in consideration of the foregoing and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Company and Investor Securityholders holding a majority of the Registrable Securities outstanding as of the date hereof, intending to be legally bound, hereby agree to amend and restate the Prior Registration Rights Agreement as follows:

1. Definitions. Capitalized terms used herein and not otherwise defined in the Agreement shall have the following meanings:

“Affiliate” means, with respect to any specified Person, any other Person who or which, directly or indirectly, controls, is controlled by, or is under common control with such specified Person, including without limitation any partner, officer, director, manager or employee of such Person.

“Commission” means the United States Securities and Exchange Commission.

“Common Stock” means the common stock, $0.01 par value per share, of the Company.

“Exchange Act” means the Securities Exchange Act of 1934, as amended, and the rules and regulations promulgated thereunder, as the same shall be in effect from time to time.

“Investors” means, collectively, (a) the Prior Investors, and (b) each other holder of the Company’s securities who executed and delivered, prior to the date of this Agreement and with the prior consent of the Company, the Prior Registration Rights Agreement, to the extent, in each case, that any such person continues to hold Registrable Securities.

“Investor Securityholders” means, collectively, (a) the Investors, and (b) any Person to whom an Investor hereafter transfers registration rights in accordance with the terms of this Agreement.

“IPO” means the Company’s first underwritten public offering of its Common Stock under the Securities Act.

“managing underwriter” shall have the meaning assigned to such term in Section 2(d) hereof.

“Person” means a natural person or any legal entity including, but not limited to, an unincorporated association, corporation, general partnership, joint venture, limited partnership, limited liability company, trust, or other entity.

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“Preferred Stock” means, collectively, Series A Preferred Stock, Series B Preferred Stock, Series C Preferred Stock, and Series D Preferred Stock.

“Register,” “registered,” and “registration” refer to a registration effected by preparing and filing with the Commission a registration statement in compliance with the Securities Act, and the declaration or ordering of effectiveness of such registration statement by the Commission.

“Registrable Securities” means, collectively, (a) shares of Common Stock issued or issuable upon conversion of shares of Preferred Stock, and (b) shares of Common Stock issued or issuable upon exercise of any of the Warrants following the completion of an IPO, and (c) shares of Common Stock issued or issuable as (or issuable upon the conversion or exercise of any warrant, right, or other security that is issued as) a stock dividend in connection with a stock split, combination of shares, recapitalization, merger, consolidation or other reorganization or otherwise with respect to Registrable Securities. Registrable Securities shall cease to be Registrable Securities upon the earlier to occur of the following: (i) a registration statement with respect to the sale of such securities shall have become effective under the Securities Act and such securities shall have been disposed of in accordance with such registration statement; (ii) the owner of such securities is able to sell all of such securities in a three-month period pursuant to Rule 144 under the Securities Act (without giving effect to Rule 144(k) thereunder); (iii) such securities shall become eligible for sale pursuant to Rule 144(k) under the Securities Act; or (iv) such securities shall have been otherwise transferred pursuant to the Securities Act or an available exemption therefrom, new certificates therefor not bearing a legend restricting further transfer shall have been delivered by the Company, and subsequent disposition of such securities shall not require the registration or qualification of such securities under the Securities Act or any similar state law then in effect.

“Registration Expenses” means all expenses (other than Selling Expenses) incident to the Company’s performance of or compliance with this Agreement and the completion of transactions relating thereto, including, without limitation, all registration and filing fees, all fees and expenses of complying with securities or blue sky laws, all printing expenses, the fees and disbursements of the Company’s independent public accountants, including the expenses of any special audits, reviews, compilations or other reports or information required by or incident to such performance and compliance, the reasonable fees or expenses of counsel for the Company, and the reasonable fees and expenses of one special counsel to represent the Investor Securityholders, as a group, on whose behalf Registrable Securities are being registered.

“Requesting Securityholders” shall have the meaning assigned to such term in Section 2(a) hereof.

“Rule 144” and “Rule 144(k)” mean, respectively, Rule 144 and Rule 144(k) promulgated by the Commission under the Securities Act or similar or successor rules.

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“Securities Act” means the Securities Act of 1933, as amended, and the rules and regulations promulgated thereunder, as the same shall be in effect from time to time.

“Selling Expenses” means all underwriting discounts, selling commissions, and stock transfer taxes applicable to the sale of Registrable Securities, and fees and disbursements of counsel for any individual Investor Securityholder, all of which shall be borne by the Investor Securityholder on whose behalf such Registrable Securities are being registered.

“Shelf Registration Notice” shall have the meaning assigned to such term in Section 3(a)(i) hereof.

“Shelf Registration Statement” shall have the meaning assigned to such term in Section 3(a) hereof.

2. Demand Registration. (a) Following the date that is 180 days after the completion of an IPO, upon the written request of Investor Securityholders holding a majority of the Registrable Securities then held by all Investor Securityholders (the “Requesting Securityholders”), requesting that the Company effect the registration of all or a portion of the Registrable Securities then held by the Requesting Securityholders, the Company will thereupon use commercially reasonable efforts to file, as promptly as reasonably practicable, a registration statement with the Commission and thereafter will use commercially reasonable efforts to effect the registration of the Registrable Securities which the Company has been so requested to register by such Requesting Securityholders, provided, however, that:

(i) when the Company is not eligible to use a Shelf Registration Statement, such Requesting Securityholders’ request for registration relate to Registrable Securities that have an aggregate anticipated price to the public of at least $10,000,000 (before Selling Expenses), and

(ii) when the Company is eligible to use a Shelf Registration Statement, such Requesting Securityholders’ request for registration relate to Registrable Securities that have an aggregate anticipated price to the public of at least $5,000,000 (before Selling Expenses).

Following receipt of such notice from the Requesting Securityholders, the Company shall, within ten (10) days following the date such request is received by the Company, notify, pursuant to Section 4 hereof, all Investor Securityholders from whom requests for registration were not initially received, and such holders shall be entitled, provided that a holder notifies the Company within 20 days of the date notice is given by the Company, to request that the Company include in the registration all or a portion of their Registrable Securities. Each registration requested pursuant to this Section 2(a) shall be (i) effected by the filing of a registration statement with the Commission on Form S-1 or a Shelf Registration Statement, and (ii) filed pursuant to Rule 415 under the Securities Act (or an equivalent rule then in effect) if so requested by the Requesting Securityholders, or the Company otherwise deems it appropriate.

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(b) Notwithstanding the foregoing, the Company shall not be obligated to effect, or take any action to effect, any registration pursuant to Section 2(a) under the following circumstances:

(i) if the Company shall have previously effected a registration, notice of which shall have been given to all Investor Securityholders holding Registrable Securities pursuant to Section 4 hereof, and all Investor Securityholders wishing to do so were permitted to register all Registrable Securities they requested to register, then the Company shall not be required to effect a registration pursuant to Section 2(a) until a period of 180 days shall have elapsed from the effective date of the most recent such previous registration; or

(ii) after the Company shall have effected four (4) registrations requested by Investor Securityholders pursuant to Section 2(a) hereof; or

(iii) if the Company shall have previously effected two (2) registrations requested by Investor Securityholders pursuant to Section 2(a) hereof during the 12-month period immediately preceding the Company’s receipt or a request for registration pursuant to Section 2(a).

(c) The Company will pay all Registration Expenses in connection with each registration of Registrable Securities effected by the Company pursuant to Section 2(a) hereof.

(d) If the registration so requested by the Requesting Securityholders involves an offering of the securities so being registered to be distributed (on a firm commitment basis) by or through one or more underwriters of recognized standing under underwriting terms appropriate for such a transaction, and the lead managing underwriter (the “managing underwriter”) of such underwritten offering informs the Company that, in its opinion, marketing factors make it advisable to reduce the number of Registrable Securities to be included in the distribution under this Section 2, then the Company will notify the Requesting Securityholders and the other requesting Investor Securityholders of the same, and then will include in the registration not more than the maximum number of shares that the managing underwriter deems advisable, any such reduction in the number of Registrable Securities shall be made first among the Investor Securityholders other than the Requesting Securityholders and then, if further reductions are required, among the Requesting Securityholders, in each case in proportion to their respective holdings of Registrable Securities; provided that if such reductions result in the Requesting Securityholders being able to sell less than 50% of the Registrable Securities that were the subject of the requested registration, upon such reduction the holders of Registrable Securities shall be granted an additional right to demand registration of such securities under this Section.

(e) Notwithstanding the foregoing obligations, if the Company notifies the Investor Securityholders requesting a registration pursuant to Section 2(a) that, in the good faith judgment of the Company, it would be materially detrimental to the Company for such registration statement to either become effective or remain effective for as long as such registration statement otherwise would be required to remain effective, or both, then the Company shall have the right to defer taking action with respect to such filing for a period of not

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more than 90 days after the initial request of the Requesting Securityholders is received by the Company; provided, however, that the Company may not invoke this right more than once in any twelve (12) month period.

(f) If requested by the underwriters for any underwritten offering of Registrable Securities pursuant to a registration requested under Section 2(a), the Company and all Investor Securityholders proposing to distribute their Registrable Securities through such underwriting will enter into an underwriting agreement with such underwriters in form and substance reasonably satisfactory to the Company, such agreement to contain such representations and warranties by the Company and such Investor Securityholders and such other terms and provisions as are customarily contained in underwriting agreements with respect to secondary distributions, including, without limitation, customary indemnification and contribution provisions. If any Investor Securityholder who has requested inclusion of Registrable Securities pursuant to Section 2(a) disapproves of the terms of the underwriting agreement or the underwriting, such holder may elect to withdraw therefrom by notifying the Company and the managing underwriter. The Registrable Securities so withdrawn shall also be withdrawn from registration.

(g) If, at any time after requesting registration pursuant to Section 2(a) and prior to the effective date of the registration statement filed in connection with such registration request, Requesting Securityholders holding a majority of the Registrable Securities to be registered shall determine for any reason not to register such Registrable Securities, such Requesting Securityholders may, at their election, give written notice of such determination to the Company. The Company shall then be relieved of its obligations to register any Registrable Securities in connection with such Requesting Securityholders’ registration request, and the Requesting Securityholders shall forfeit their right to one demand registration statement pursuant to this Section 2 (but the Company shall not be relieved of its obligation to pay the Registration Expenses in connection therewith as provided in Section 2(c) hereof).

(h) In connection with the first request for registration pursuant to Section 2(a), the Company may, within 10 days after its receipt of such request, give the Requesting Securityholders notice that it is the good faith intention of the Company to register securities for sale for its own account. Thereafter, the provisions of Section 4 shall govern, and the Requesting Securityholders’ registration request under Section 2(a) shall be deemed rescinded. The Requesting Securityholders shall again be entitled to request such registration under Section 2(a), but not sooner than the earlier of (i) 180 days after the effective date of the Company’s registration of securities for its own account, and (ii) the Company’s determination (of which the Company shall promptly notify the holders of Registrable Securities) not to proceed with its registration of securities.

3. Shelf Registration. (a) During any time that the Company is eligible to file a registration statement on Form S-3 (such form, and any successor or similar short-form registration statement, herein referred to as a “Shelf Registration Statement”), subject to the limitations herein, the Investor Securityholders holding a majority of the Registrable Securities held by all Investor Securityholders may request, in writing, that the Company file a Shelf

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Registration Statement with respect to the Registrable Securities held by Investor Securityholders who make such request of the Company, specifying in each case the number of Registrable Securities to be included in the Shelf Registration Statement. If the Company receives such a request, then the Company shall:

(i) within ten (10) days following the date such request is received by the Company, give notice of the proposed registration (a “Shelf Registration Notice”) to all Investor Securityholders (other than those initiating the request under this Section 3); and

(ii) as soon as practicable, use commercially reasonable efforts to file such Shelf Registration Statement with the Commission and have such Shelf Registration Statement declared effective by the Commission covering the Registrable Securities specified in the request, together with such Registrable Securities of any other Investor Securityholder joining in such request as are specified in a request received by the Company within twenty (20) days after the Shelf Registration Notice is given; and

(iii) use commercially reasonable efforts to cause the registration statement or statements filed pursuant to this Section 3 to remain effective until the earlier of (A) the date on which all Registrable Securities shall have been sold or (B) the date on which all Registrable Securities cease to be Registrable Securities hereunder.

(b) Notwithstanding the foregoing, the Company shall not be obligated to effect, or take any action to effect, any registration pursuant to this Section 3 under the following circumstances:

(i) if Form S-3 is not then available or becomes unavailable for such offering by the Investor Securityholders; or

(ii) if the Investor Securityholders who request that the Company file a Shelf Registration Statement with the Commission, together with Investor Securityholders requesting to participate in response to the Shelf Registration Notice, propose to sell Registrable Securities having an aggregate anticipated price to the public of less than $10,000,000 (before Selling Expenses); or

(iii) if the Company notifies the Investor Securityholders requesting registration pursuant to this Section 3 that, in the good faith judgment of the Company, it would be materially detrimental to the Company for such Shelf Registration Statement to either become effective or remain effective for as long as such Shelf Registration Statement otherwise would be required to remain effective, or both, in which case the Company shall have the right to defer taking action with respect to such filing for a period of not more than 90 days after the request of the initiating Investor Securityholders is received by the Company; provided, however, that the Company shall not invoke this right more than once in any twelve (12) month period; or

(iv) if the Company has, within the twelve (12) month period preceding the date of such request, already filed two (2) Shelf Registration Statements for the Investor Securityholders pursuant to this Section 3; or

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(v) during the period ending one hundred eighty (180) days after the effective date of a registration made under Section 2 hereof or a registration described in Section 2(b)(i) hereof.

(c) The Company will pay all Registration Expenses in connection with each registration of Registrable Securities effected by the Company pursuant to this Section 3.

(d) The provisions of Sections 2(d) and 2(f) hereof shall apply to underwritten public offerings pursuant to a Shelf Registration Statement.

4. Piggy-Back Registrations. (a) If, at any time commencing 180 days following the completion of an IPO, the Company proposes to register any of its shares of Common Stock, whether or not for sale for its own account, in connection with the public offering of such securities solely for cash, on a form and in a manner which would permit registration of Registrable Securities for sale to the public under the Securities Act, the Company will give prompt written notice each such time to all holders of Registrable Securities of its intention to do so, describing such securities and specifying the form and manner and the other relevant facts involved in such proposed registration. Upon the written request of any such holder to register any or all of such holder’s Registrable Securities received by the Company within 20 days after such notice is given by the Company (which request shall specify the Registrable Securities intended to be disposed of by such holder), the Company will use commercially reasonable efforts to effect the registration under the Securities Act of all Registrable Securities which the Company has been so requested to register by the holders of Registrable Securities, to the extent required to permit the disposition of the Registrable Securities so to be registered, provided, however, that:

(b) Notwithstanding any other provision of this Section 4, if the managing underwriter of any registered underwritten public offering initiated by the Company informs the Company that, in its opinion, marketing factors make it advisable to reduce the number of shares of Common Stock proposed to be registered by Persons other than the Company, then the Company may exclude from such registration and underwriting all or a portion of the Registrable Securities which would otherwise be registered and underwritten pursuant to this Section 4. The Company shall so advise all holders of securities requesting registration of any limitations on the number of shares to be underwritten and the number of shares of Common Stock that may be included in the registration; provided that the reduction of shares included in the registration and underwriting shall be allocated in the following manner:

first, the securities (other than Registrable Securities) of the Company held by officers and directors of the Company shall be excluded from such registration and underwriting to the extent required by such limitation, and if a limitation on the number of shares is still required, then

next, the securities held by any holder of Common Stock not having any contractual, incidental registration rights shall be excluded from such registration and underwriting to the extent required by such limitation, and if a limitation on the number of shares is still required, then

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next, the securities (other than Registrable Securities) of the Company held by Persons who have registration rights under any agreement with the Company (other than this Agreement) shall be excluded from such registration and underwriting to the extent required by such limitation, and, if a limitation on the number of shares is still required, then

next, the number of shares that may be included in the registration and underwriting shall be allocated pro rata among all holders of Registrable Securities in proportion, as nearly as practicable, to the respective amounts of Registrable Securities requested by them to be included in such registration and underwriting, and the Company shall be obligated to include in such registration statement only such limited portion (which may be none) of the Registrable Securities as the managing underwriter determines in good faith is advisable.

(c) If, at any time after giving such written notice of its intention to register any of its securities and prior to the effective date of the registration statement filed in connection with such registration, the Company shall determine for any reason and in its sole discretion to withdraw any registration referred to in this Section 4, the Company may, at its election, give written notice of such determination to each holder of Registrable Securities who has requested Registrable Securities to be included, and thereupon the Company shall be relieved of its obligation to register any Registrable Securities in connection with such registration (but not from its obligation to pay the Registration Expenses in connection therewith as provided in Section 4(e) below), without prejudice however to the rights of the Investor Securityholders to request that such registration be effected as a registration under Section 2(a) hereof;

(d) the Company shall not be obligated to effect any registration of Registrable Securities under this Section 4:

(i) incidental to the registration of any of its securities in connection with (A) dividend reinvestment plans or stock option or other employee benefit plans, or (B) business combination transactions or any other similar transaction, the purpose of which is not to raise capital, or

(ii) pursuant to a so-called “unallocated or “universal” shelf registration statement.

(e) The Company will pay all Registration Expenses in connection with each registration of Registrable Securities requested pursuant to this Section 4.

5. Registration Procedures. (a) If and whenever the Company is required to effect the registration of any Registrable Securities as provided in Sections 2, 3 or 4 hereof, the Company will use commercially reasonable efforts to expeditiously:

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(i) prepare and promptly file with the Commission (in any event within 60 days after a request for registration has been received by the Company) a registration statement with respect to such Registrable Securities and use commercially reasonable efforts to cause such registration statement to become effective;

(ii) prepare and file with the Commission such amendments and supplements to such registration statement and the prospectus used in connection therewith as may be necessary to keep such registration statement effective and to comply with the provisions of the Securities Act with respect to the disposition of all Registrable Securities and other securities covered by such registration statement until the earliest of such time as all of such Registrable Securities and other securities have been disposed of in accordance with the intended methods of disposition by the seller or sellers thereof set forth in such registration statement, or the expiration of six months after such registration statement becomes effective, or such time as all the Registrable Securities registered pursuant to such registration statement cease to be Registrable Securities;

(iii) furnish to each seller of such Registrable Securities, without charge, such number of conformed copies of such registration statement and of each such amendment and supplement thereto, such number of copies of the prospectus included in such registration statement (including each preliminary prospectus and any summary prospectus), in conformity with the requirements of the Securities Act, such documents incorporated by reference in such registration statement or prospectus, and such other documents, as such seller may reasonably request;

(iv) register or qualify all Registrable Securities and other securities covered by such registration statement under the securities or “blue sky” laws of such jurisdictions as the sellers (or in an underwritten offering, the managing underwriter) shall reasonably request, and do any and all other acts and things which may be necessary or advisable under the securities or “blue sky” laws to enable such sellers to consummate the disposition in such jurisdictions of their Registrable Securities covered by such registration statement, except that the Company shall not for any such purpose be required to qualify generally to do business as a foreign corporation in any jurisdiction wherein it is not so qualified, or to subject itself to taxation in any such jurisdiction, or to consent to general service of process in any such jurisdiction;

(v) furnish to each seller of Registrable Securities by means of such registration a signed counterpart, addressed to such seller, of (A) a copy of an opinion of counsel for the Company, dated the effective date of such registration statement (or, if such registration includes an underwritten public offering, dated the date of the closing under the underwriting agreement and (B) a copy of a “comfort” letter dated the effective date of such registration statement (and, if such registration statement includes an underwritten public offering, dated the date of the closing under the underwriting agreement) signed by the independent public accountants who have certified the Company’s financial statements included in such registration statement, covering substantially the same matters with respect to such registration statement (and the prospectus included therein) and, in the case of such accountants’ letter, with respect to events subsequent to the date of such financial statements, as are customarily covered in opinions of issuer’s counsel and in accountants’ letters for registrations of the type involved;

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(vi) notify each seller of Registrable Securities covered by such registration statement, at any time when a prospectus relating thereto is required to be delivered under the Securities Act, of the happening of any event as a result of which the prospectus included in such registration statement, as then in effect, includes an untrue statement of a material fact or omits to state any material fact required to be stated therein or necessary to make the statements therein not misleading in the light of the circumstances then existing, and at the request of any such seller prepare and furnish to such seller a reasonable number of copies of a supplement to or an amendment of such prospectus as may be necessary so that, as thereafter delivered to the purchasers of such Registrable Securities or other securities, such prospectus shall not include an untrue statement of a material fact or omit to state a material fact required to be stated therein or necessary to make the statements therein not misleading in the light of the circumstances then existing;

(vii) otherwise use commercially reasonable efforts to comply with all applicable rules and regulations of the Commission, and make available to its securities holders, as soon as reasonably practicable, an earnings statement covering the period of at least 12 months, but not more than 18 months, beginning with the first month of the first fiscal quarter after the effective date of such registration statement, which earnings statement shall satisfy the provisions of Section 11(a) of the Securities Act and the rules and regulations of the Commission thereunder, including Rule 158; and

(viii) use commercially reasonable efforts to list such securities on each securities exchange on which the equity securities of the Company are then listed, if such securities are not already so listed and if such listing is then permitted under the rules of such exchange, and, if necessary, provide a transfer agent and registrar for such Registrable Securities not later than the effective date of such registration statement.

It shall be a condition to the Company’s obligations to effect the registration of Registrable Securities under Section 2, 3 and 4 hereof that each holder of Registrable Securities as to which registration is being effected furnish to the Company such information regarding such holder and the distribution of such securities as the Company may from time to time reasonably request in connection with the filing of the relevant registration statement and in connection with maintaining its effectiveness.

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(b) If the Company at any time proposes to register any of its securities under the Securities Act (other than pursuant to a request made under Section 2 hereof), whether or not for sale for its own account, and such securities are to be distributed by or through one or more underwriters, the Company will make reasonable efforts, if requested by any holder of Registrable Securities who requests registration of Registrable Securities in connection therewith pursuant to Section 4 hereof, to arrange for such underwriters to include such Registrable Securities among those securities to be distributed by or through such underwriters, subject to the terms and conditions of this Agreement.

(c) Whenever a registration requested pursuant to Section 2 is for an underwritten offering, the Company shall have the right to select the managing underwriter to administer the offering. If the Company at any time proposes to register any of its securities under the Securities Act for sale for its own account and such securities are to be distributed by or through one or more underwriters, the managing underwriter shall be selected by the Company.

6. Preparation; Reasonable Investigation. In connection with the preparation and filing of each registration statement registering Registrable Securities under the Securities Act, the Company will give one representative selected by the holders of Registrable Securities on whose behalf such Registrable Securities are to be so registered and their underwriters, if any, and their counsel, the opportunity, upon reasonable request, to review and comment upon such registration statement, each prospectus included therein or filed with the Commission, and each amendment thereof or supplement thereto, and will give each of such representative, underwriters and counsel, such reasonable access to its books and records and such opportunities to discuss the business of the Company with its officers, counsel and the independent public accountants who have certified its financial statements as they shall reasonably request.

7. Indemnification; Contribution. (a) In the event of any registration of any securities of the Company under the Securities Act, the Company will, and hereby does, indemnify and hold harmless in the case of any registration statement filed pursuant to Section 2, 3 or 4 hereof, the holder of any Registrable Securities covered by such registration statement, its directors and officers, each officer and director of each underwriter, each other person who participates as an underwriter in the offering or sale of such securities and each other person, if any, who controls such holder or any such underwriter within the meaning of the Securities Act against any losses, claims, damages, liabilities and expenses, joint or several, to which such holder or any such director or officer or participating or controlling person may become subject under the Securities Act or otherwise, insofar as such losses, claims, damages, liabilities or expenses (or actions or proceedings or investigations in respect thereof) arise out of or are based upon (x) any untrue statement or alleged untrue statement of any material fact contained in any registration statement under which such securities were registered under the Securities Act, any preliminary prospectus (unless, with respect to the indemnification of the officers and directors of each underwriter and each other person participating as an underwriter, any such statement is corrected in a subsequent prospectus and the underwriters are given the opportunity to circulate the corrected prospectus to all persons receiving the preliminary prospectus), final prospectus or summary prospectus included therein, or any amendment or supplement thereto, or any

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document incorporated by reference therein, or (y) any omission or alleged omission to state therein a material fact required to be stated therein or necessary to make the statements therein not misleading, or (z) any violation by the Company of any securities laws in connection with such registration, and the Company will reimburse such holder and each such director, officer, participating person and controlling person for any legal or any other expenses reasonably incurred by them in connection with investigating or defending any such loss, claim, liability, action or proceeding; provided, however, that the Company shall not be liable to any seller, director, officer, participating person or controlling person in any such case to the extent that any such loss, claim, damage, liability (or action or proceeding in respect thereof) or expense arises out of or is based upon an untrue statement or alleged untrue statement or omission or alleged omission made in such registration statement, any such preliminary prospectus, final prospectus, summary prospectus, amendment or supplement in reliance upon and in conformity with written information furnished to the Company in an instrument prepared by or under the direction of such seller, director, officer, participating person or controlling person for use in the preparation of such documents, which information was specifically stated to be for use in the registration statement, prospectus, offering circular or other document. Such indemnity shall remain in full force and effect regardless of any investigation made by or on behalf of such seller or any such director, officer, participating person or controlling person and shall survive the transfer of such securities by such seller. The Company shall agree to provide for contribution relating to such indemnity as shall be reasonably requested by any seller of Registrable Securities or the underwriters.

(b) The Company may require, as a condition to including any Registrable Securities in any registration statement filed pursuant to Section 2(a), that the Company shall have received an undertaking satisfactory to it from the prospective sellers of such securities and their underwriters, to indemnify and hold harmless (in the same manner and to the same extent as set forth in subdivision (a) of this Section 7) the Company, each director of the Company, each officer of the Company who shall sign such registration statement and each other person, if any, who controls the Company within the meaning of the Securities Act, with respect to any statement in or omission from such registration statement, any preliminary prospectus, final prospectus or summary prospectus included therein, or any amendment or supplement thereto, but only if such statement or omission was made in reliance upon and in conformity with written information furnished to the Company through an instrument prepared by or under the direction of such sellers or their underwriters specifically stating that it is for use in the preparation of such registration statement, preliminary prospectus, final prospectus, summary prospectus, amendment or supplement, and provided that (i) the obligation to provide indemnification pursuant to this Section 7(b) shall be several, and not joint and several, among such sellers and (ii) the liability of each seller hereunder shall be limited to the proportion of any such loss, claim, damage, liability or expense which is equal to the proportion that the public offering price of the shares sold by such seller under such registration statement bears to the total public offering price of all securities sold thereunder, but not in any event to exceed the net proceeds received by such seller from the sale of Registrable Securities covered by such registration statement. Such indemnity shall remain in full force and effect regardless of any investigation made by or on behalf of the Company or any such director, officer or controlling person and shall survive the transfer of such securities by such sellers.

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(c) Promptly after receipt by an indemnified party of notice of the commencement of any action or proceeding involving a claim referred to in the preceding subdivisions of this Section 7, such indemnified party will, if a claim in respect thereof is to be made against an indemnifying party, give written notice to the latter of the commencement of such action; provided, however, that the failure of any indemnified party to give notice as provided herein shall not relieve the indemnifying party of its obligations under the preceding subdivisions of this Section 7 except to the extent that the indemnifying party is materially prejudiced as a result of such failure to give notice. In case any such action is brought against an indemnified party, the indemnifying party shall be entitled to participate in and to assume the defense thereof, jointly with any other indemnifying party similarly notified, to the extent that it may wish, with counsel reasonably satisfactory to such indemnified party. After notice from the indemnifying party to such indemnified party of its election so to assume the defense thereof, the indemnifying party shall not be liable to such indemnified party for any legal or other expenses subsequently incurred by the indemnified party in connection with the defense thereof unless (i) the indemnifying party shall have failed to retain counsel for the defense of such claim(s) as aforesaid, (ii) the indemnifying party and the indemnified party shall have mutually agreed to the retention of separate counsel for the indemnified party, or (iii) the indemnified party shall have reasonably concluded that there may be legal defenses available to it which are different from or additional to those available to the indemnifying party (in which case the indemnifying party shall not have the right to direct the defense of such action on behalf of the indemnified party); provided, however, in no event shall the indemnifying party be liable for the reasonable expenses of more than one counsel for all indemnified parties. No indemnifying party will consent to entry of any judgment or enter into any settlement which does not include as an unconditional term thereof the giving by the claimant or plaintiff to such indemnified party of a release from all liability in respect to such claim or litigation. The indemnifying party shall not be liable for any settlement of any proceeding effected without the written consent of such indemnifying party, such consent not to be unreasonably withheld or delayed, but if settled with such consent or if there be a final judgment for the plaintiff, the indemnifying party agrees to indemnify each indemnified party from and against any loss or liability by reason of such settlement or judgment.

(d) Indemnification similar to that specified in this Section 7 (with appropriate modifications) shall be given by the Company and each seller of Registrable Securities with respect to any required registration or other qualification of such Registrable Securities under any federal or state law or regulation.

8. Rule 144 Reporting. With a view to making available the benefits of certain rules and regulations of the Commission which may at any time permit the sale of the Registrable Securities to the public without registration (but in no way reducing the rights of the holders of such Registrable Securities) at all times after 90 days after any registration statement covering a public offering of securities of the Company under the Securities Act shall have become effective, or at all times after the equity securities of the Company shall initially be registered pursuant to the requirements of Section 12 of the Exchange Act, the Company agrees at its cost and expense to use its best efforts to:

(a) make and keep public information available, as those terms are understood within Rule 144 under the Securities Act;

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(b) file with the Commission in a timely manner all reports and other documents required of the Company under the Securities Act and the Exchange Act;

(c) furnish to each holder of Registrable Securities, promptly upon request, a written statement by the Company as to its compliance with the reporting requirements of such Rule 144 and of the Securities Act and the Exchange Act, a copy of the most recent annual and/or quarterly report of the Company, and such other reports and documents so filed by the Company with the Commission as such holder may reasonably request in availing itself of any rule or regulation of the Commission allowing such holder to sell any Registrable Security without registration; and

(d) furnish to each holder of Registrable Securities which is a “qualified institutional buyer” within the meaning of Rule 144A under the Securities Act, promptly upon written request from such holder, such information as may be required under Rule 144A for delivery to any prospective purchaser of any Registrable Securities in order to permit such holder to avail itself of the benefits of the exemptions under the Securities Act afforded by such Rule.

9. Transfer of Registration Rights. The registration rights held by any Investor Securityholder who or which is a party to this Agreement as of the date hereof may be transferred to any Person who acquires at least 50% of the Registrable Securities (such percentage to be determined assuming conversion of all shares of Preferred Stock and exercise of all Warrants) held by the transferring Investor Securityholder as of the date of this Agreement; provided, however, that such 50% limitation shall not apply to transfers pursuant to domestic relations orders, for estate planning purposes, or to Affiliates of the transferor; and, further, provided, that the Company shall be provided with written notice thereof, and each transferee of registration rights hereunder shall execute and deliver a counterpart of this Agreement and become a party hereto.

10. Governing Law. THIS AGREEMENT SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF DELAWARE, WITHOUT GIVING REGARD TO THE CONFLICT OF LAWS PRINCIPLES THEREOF.

11. Notices. All notices and requests furnished pursuant to this Agreement shall be in writing, shall be made by hand-delivery, first-class mail (registered or certified, return receipt requested), confirmed facsimile or overnight air courier guaranteeing next business day delivery, and shall be sent, if to a party to this Agreement other than the Company, to such party’s address then on file with the Company, and if to the Company, to:

Amedica Corporation

615 Arapeen Drive

Suite 302

Salt Lake City, Utah 84108

Attention: Chief Executive Officer

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Except as otherwise provided in this Agreement, the date of each such notice and request shall be deemed to be, and the date on which each such notice and request shall be deemed received shall be: (a) at the time delivered, if personally delivered or mailed; (b) when receipt is acknowledged, if sent by facsimile; and (c) the next business day after timely delivery to the courier, if sent by overnight air courier guaranteeing next business day delivery.

12. Entire Agreement; Integration. This Agreement (including its schedules) supersedes all prior agreements between or among the Company and any of the other parties hereto (including, without limitation, the Prior Registration Rights Agreement), and constitutes the full and entire agreement of the parties with respect to the registration rights of the Investor Securityholders, and all such prior agreements, whether written or oral, are terminated and shall be of no further force or effect, and all rights thereunder are hereby waived.

13. Injunctive Relief. Each of the parties hereto acknowledges that in the event of a breach by any of them of any material provision of this Agreement, the aggrieved party may be without an adequate remedy at law. Each of the parties therefore agrees that in the event of such a breach hereof the aggrieved party may elect to institute and prosecute proceedings in any court of competent jurisdiction to enforce specific performance or to enjoin the continuing breach hereof. By seeking or obtaining any such relief, the aggrieved party shall not be precluded from seeking or obtaining any other relief to which it may be entitled.

14. Section Headings. Section headings are for convenience of reference only and shall not affect the meaning of any provision of this Agreement.

15. Counterparts. This Agreement may be executed in any number of counterparts, each of which shall be an original, and all of which shall together constitute one and the same instrument. All signatures need not be on the same counterpart.

16. Severability. If any provision of this Agreement shall be invalid or unenforceable, such invalidity or unenforceability shall not affect the validity and enforceability of the remaining provisions of this Agreement, unless the result thereof would be unreasonable, in which case the parties hereto shall negotiate in good faith as to appropriate amendments hereto.

17. Amendments and Waivers. This Agreement may be terminated, or any term or provision hereof may be amended, and the observance of any provision of this Agreement may be waived (either generally or in a particular instance, and either retroactively or prospectively) only with the written consent of the Company and Investor Securityholders holding a majority of the Registrable Securities then outstanding (such majority to be determined assuming conversion of all shares of Preferred Stock then convertible into Registrable Securities and exercise of all Warrants then exercisable for Registrable Securities then held by the Investor Securityholders). Any amendment, termination, or waiver effected in accordance with this Section 17 shall be binding on all parties hereto, regardless of whether any such party has

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consented thereto. No waivers of or exceptions to any term, condition, or provision of this Agreement, in any one or more instances, shall be deemed to be or construed as a further or continuing waiver of any such term, condition, or provision.

18. Filing. A copy of this Agreement and of all amendments thereto shall be filed at the principal executive office of the Company with the Secretary of the Company.

19. Termination. Unless sooner terminated pursuant to amendment adopted in accordance with Section 17 hereof, this Agreement (other than Section 7 hereof) shall terminate in its entirety on such date as there shall be no Registrable Securities outstanding.

20. No Third Party Beneficiaries. Nothing herein expressed or implied is intended to confer upon any person, other than the parties hereto or their respective permitted transferees of registration rights, any rights, remedies, obligations or liabilities under or by reason of this Agreement.

21. Aggregation of Registrable Securities. All shares of Registrable Securities held or acquired by Affiliates shall be aggregated together for the purpose of determining the availability of any rights under this Agreement.

22. Confidentiality. Each Investor Securityholder agrees that such Investor Securityholder will keep confidential and will not disclose, divulge, or use for any purpose (other than to monitor its investment in the Company) any confidential information obtained from the Company pursuant to the terms of this Agreement (including notice of the Company’s intention to file a registration statement), unless such confidential information (a) is known or becomes known to the public in general (other than as a result of a breach of this Section 22 by such Investor Securityholder), or (b) is or has been made known or disclosed to the Investor Securityholder by a third party without a breach of any obligation of confidentiality such third party may have to the Company; provided, however, that an Investor Securityholder may disclose confidential information (i) to its attorneys, accountants, consultants, and other professionals to the extent necessary to obtain their services in connection with monitoring its investment in the Company; (ii) to any prospective permitted transferee of registration rights from such Investor Securityholder, if such prospective purchaser agrees to be bound by the provisions of this Section 22; (iii) to any Affiliate, partner, member, stockholder, or wholly owned subsidiary of such Investor Securityholder in the ordinary course of business, provided that such Investor Securityholder informs such Person that such information is confidential and directs such Person to maintain the confidentiality of such information; or (iv) as may otherwise be required by law, provided that the Investor Securityholder promptly notifies the Company of such disclosure and takes reasonable steps to minimize the extent of any such required disclosure.

[REMAINDER INTENTIONALLY BLANK, SIGNATURES FOLLOW]

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IN WITNESS WHEREOF, this Third Amended and Restated Registration Rights Agreement has been duly executed by the parties hereto, effective as of the date first written above.

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INVESTOR:

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Schedule A

PRIOR INVESTORS