CAPNIA, INC. CONVERTIBLE PROMISSORY NOTE

Exhibit 4.6

THIS NOTE AND THE UNDERLYING SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “ACT”), OR UNDER THE SECURITIES LAWS OF ANY STATE. THESE SECURITIES MAY NOT BE OFFERED, SOLD OR OTHERWISE TRANSFERRED, PLEDGED OR HYPOTHECATED EXCEPT AS PERMITTED UNDER THE ACT AND APPLICABLE STATE SECURITIES LAWS IN ACCORDANCE WITH APPLICABLE REGISTRATION REQUIREMENTS OR AN EXEMPTION THEREFROM. THE ISSUER OF THESE SECURITIES MAY REQUIRE AN OPINION OF COUNSEL REASONABLY SATISFACTORY TO THE ISSUER THAT SUCH OFFER, SALE, TRANSFER, PLEDGE OR HYPOTHECATION OTHERWISE COMPLIES WITH THE ACT AND ANY APPLICABLE STATE SECURITIES LAWS.

CAPNIA, INC.

CONVERTIBLE PROMISSORY NOTE

FOR VALUE RECEIVED CAPNIA, INC., a Delaware corporation (the “Company”), promises to pay to                    (the “Holder”), or its registered assigns, the principal amount of $            , or such lesser amount as shall equal the outstanding principal amount hereof, together with compound interest from the date of this Note on the unpaid principal balance at a rate equal to 12% per annum, compounded on the first day of each month and computed on the basis of the actual number of days elapsed and a year of 365 days. Two times the unpaid principal, together with any then accrued but unpaid interest and any other amounts payable hereunder, shall be due and payable on the earlier of (i) upon demand made after February 10, 2011 (the “Maturity Date”) by Holders representing at least a majority of the principal amount of all then outstanding Notes issued pursuant to that certain Convertible Note and Warrant Purchase Agreement by and among the Company and the Investors described therein, dated as of February 10, 2010, (as the same may from time to time be amended, modified or supplemented, the “Purchase Agreement”), or (ii) when, upon or after the occurrence of an Event of Default (as defined below), such amounts are declared due and payable by the Holder or made automatically due and payable in accordance with the terms of this Note. This Note is one of the “Notes” issued pursuant to the Purchase Agreement. Capitalized terms not otherwise defined herein shall have the meaning set forth in the Purchase Agreement.

THE OBLIGATIONS DUE UNDER THIS NOTE ARE SECURED BY A SECURITY AGREEMENT (THE “SECURITY AGREEMENT”) DATED AS OF THE DATE HEREOF AND EXECUTED BY THE COMPANY FOR THE BENEFIT OF HOLDER. ADDITIONAL RIGHTS OF HOLDER ARE SET FORTH IN THE SECURITY AGREEMENT.

The following is a statement of the rights of the Holder of this Note and the conditions to which this Note is subject, and to which the Holder, by the acceptance of this Note, agrees:

1. Certain Definitions.

(a) “Change of Control” means, unless otherwise determined in writing by the holders of at least two-thirds of the Company’s Preferred Stock then outstanding, (X) the acquisition of the Company by another entity by means of any transaction or series of related transactions (including, without limitation, any merger, consolidation or other form of reorganization) in which outstanding shares of the Company are exchanged for or converted into securities or other consideration issued, or caused to be issued, by the acquiring entity or its affiliate, unless the Company’s stockholders of record as constituted immediately prior to such transaction or series of related transactions will, immediately after such transaction or series of related transactions, hold at least a majority of the voting power of the surviving or acquiring entity on account of shares held by them prior to such transaction or series of related transactions, or (Y) a sale, lease or other disposition of all or substantially all of the assets of the Company.

(b) “Event of Default” has the meaning given in Section 4 of this Note.

(c) “Next Financing” is a transaction or series of related transactions after the date of this Note that is approved by the board of directors of the Company in which the Company issues and sells shares of its capital stock in exchange for aggregate gross proceeds of at least $1,500,000 (excluding any amounts received upon conversion or cancellation of the Notes).

(d) “Next Financing Securities” are the equity securities issued by the Company in the Next Financing with such rights, preferences, privileges and restrictions, contractual or otherwise, as the securities issued by the Company in the Next Financing.

(e) “Note Conversion Price” means a price per share equal to 75% of the price per share paid by the other purchasers of the Next Financing Securities sold in the Next Financing.

(f) “Non-Qualified Financing” is a transaction or series of related transactions after the date of this Note that is approved by the board of directors of the Company in which the Company issues and sells shares of its capital stock in exchange for cash, conversion or cancellation of indebtedness, or any combination thereof, and which (i) does not constitute a Next Financing, or (ii) constitutes a Next Financing but occurs after the Maturity Date.

(g) “Purchase Agreement” has the meaning given in the preamble to this Note.

2. Prepayment. The Company may not prepay this Note in whole or in part, without the written consent of the Holders of at least two-thirds of the principal amount of all then outstanding Notes issued pursuant to the Purchase Agreement; provided, however, that any such prepayment will be applied first to the payment of expenses due under the Notes, second to interest accrued on the Notes and third, if the amount of prepayment exceeds the amount of all such expenses and accrued interest, to the payment of principal of the Notes, all on a pro-rata basis.

3. Conversion.

(a) Automatic Conversion upon a Next Financing prior to Maturity Date. If a Next Financing occurs on or prior to the Maturity Date, then the outstanding principal amount of this

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Note and all accrued and unpaid interest under this Note shall automatically convert into fully paid and nonassessable shares of Next Financing Securities at the Note Conversion Price, with any fractional shares rounded down. Upon the automatic conversion of this Note, the Company shall give written notice to the Holder, notifying the Holder of such conversion and specifying the Note Conversion Price, the principal amount of the Note converted and the date on which such conversion occurred and calling upon such Holder to surrender the Note to the Company. Upon such conversion, the Holder shall surrender this Note at the Company’s principal executive office, or, if this Note has been lost, stolen, destroyed or mutilated, then, in the case of loss, theft or destruction, the Holder shall deliver an indemnity agreement reasonably satisfactory in form and substance to the Company or, in the case of mutilation, the Holder shall surrender and cancel this Note. The Company shall, as soon as practicable thereafter, issue and deliver to Holder at such principal executive office a certificate or certificates for the number of shares to which the Holder shall be entitled upon such conversion (bearing such legends as are required by the Purchase Agreement and applicable state and federal securities laws in the opinion of counsel to the Company). Such conversion shall be deemed to have been made immediately prior to the close of business on the date of closing of the Next Financing, and on and after such date the person entitled to receive the shares issuable upon such conversion shall be treated for all purposes as the record holder of such shares as of such date.

(b) Voluntary Conversion. If no Next Financing takes place on or prior to the Maturity Date, then all or a portion of the outstanding principal amount of this Note and all accrued and unpaid interest under this Note shall be convertible at the option of the Holder at any time after the Maturity Date into (i) that number of shares of the Company’s Series C Preferred Stock at a price of $1.80 per share (as adjusted to reflect subsequent stock dividends, stock splits, combinations or recapitalizations), or (ii) that number of shares of the equity securities issued by the Company in a Non-Qualified Financing at a price per share equal to 75% of the price per share paid by the other purchasers of the equity securities sold in the Non-Qualified Financing. Before Holder shall be entitled to convert this Note under this Section 3(b), the Holder shall surrender this Note, duly endorsed, at the Company’s principal executive office and shall give written notice to the Company of the election to convert the same pursuant to this Section, and shall state therein the amount of the unpaid principal amount of this Note to be converted and the name or names in which the certificate or certificates for shares are to be issued. The Company shall, as soon as practicable thereafter, issue and deliver at Holder at such principal executive office a certificate or certificates for the number of shares to which the Holder shall be entitled upon conversion (bearing such legends as are required by the Purchase Agreement and applicable state and federal securities laws in the opinion of counsel to the Company), together with a replacement Note (if any principal amount is not converted) and any other securities and property to which Holder is entitled upon such conversion under the terms of this Note, including a check payable to Holder for any cash amounts payable as described in Section 3(c). The conversion shall be deemed to have been made immediately prior to the close of business on the date of the surrender of this Note, and the person entitled to receive the shares issuable upon such conversion shall be treated for all purposes as the record holder of such shares as of such date.

(c) Fractional Shares; Nonassessable; Effect of Conversion. No fractional shares shall be issued upon conversion of this Note, and in lieu of the Company issuing any fractional shares to the Holder upon the conversion of this Note, the Company shall pay to the Holder an

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amount equal to the product obtained by multiplying the Note Conversion Price by the fraction of a share not issued pursuant to this sentence. The Company covenants that the shares of Next Financing Securities issuable upon the conversion of this Note will, upon conversion of this Note, be validly issued, fully paid and nonassessable and free from all taxes, liens and charges in respect of the issue thereof. Upon conversion of this Note in full and the payment of the amounts specified in this Section 3(c), the Company shall be forever released from all its obligations and liabilities under this Note.

(d) Further Assurances. In connection with the conversion of this Note, the Holder, by acceptance of this Note, agrees to execute all agreements and other documents executed by the investors in the Next Financing.

4. Events of Default. The occurrence of any of the following shall constitute an “Event of Default” under this Note:

(a) Failure to Pay. The Company shall fail to pay (i) when due any principal payment on the due date hereunder or (ii) any interest or other payment required under the terms of this Note on the date due and such payment shall not have been made within five (5) days of the Company’s receipt of the Holder’s written notice to the Company of such failure to pay; or

(b) Voluntary Bankruptcy or Insolvency Proceedings. The Company shall (i) apply for or consent to the appointment of a receiver, trustee, liquidator or custodian of itself or of all or a substantial part of its property, (ii) commence a voluntary case or other proceeding seeking liquidation, reorganization or other relief with respect to itself or its debts under any bankruptcy, insolvency or other similar law now or hereafter in effect or consent to any such relief or to the appointment of or taking possession of its property by any official in an involuntary case or other proceeding commenced against it, (iii) make an assignment for the benefit of creditors, or (iv) take any action for the purpose of effecting any of the foregoing; or

(c) Involuntary Bankruptcy or Insolvency Proceedings. Proceedings for the appointment of a receiver, trustee, liquidator or custodian of the Company or of all or a substantial part of the Company’s property, or an involuntary case or other proceedings seeking liquidation, reorganization or other relief with respect to the Company or the Company’s debts under any bankruptcy, insolvency or other similar law now or hereafter in effect shall be commenced and an order for relief entered or such proceeding shall not be dismissed or discharged within thirty (30) days of commencement; or

(d) Breach of Representations and Warranties. Any material breach by the Company of any of the representations or warranties contained in Section 3 of the Purchase Agreement; or

(e) Failure to Pay Obligations. The Company generally fails to pay its obligations as and when due or if any judgment is secured against the Company, which judgment is not satisfied within ten (10) days.

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Upon the occurrence or existence of any Event of Default described in Section 4(a), (d) and (e) and at any time thereafter during the continuance of such Event of Default, the Holder may, with the consent of the Holders of at least two-thirds of the principal amount of all then outstanding Notes issued pursuant to the Purchase Agreement, by written notice to Company, declare this Note immediately due and payable without presentment, demand, protest or any other notice of any kind, all of which are hereby expressly waived, anything contained in this Note to the contrary notwithstanding. Upon the occurrence or existence of any Event of Default described in Sections 4(b) and (c), immediately and without notice, this Note shall automatically become immediately due and payable, without presentment, demand, protest or any other notice of any kind, all of which are hereby expressly waived, anything contained in this Note to the contrary notwithstanding. In addition to the foregoing remedies, upon the occurrence or existence of any Event of Default, the Holder may exercise any other right, power or remedy permitted to it by law.

5. Miscellaneous.

(a) Loss, Theft, Destruction or Mutilation of Note. Upon receipt of evidence reasonably satisfactory to the Company of the loss, theft, destruction or mutilation of this Note and, in the case of loss, theft or destruction, delivery of an indemnity agreement reasonably satisfactory in form and substance to the Company or, in the case of mutilation, on surrender and cancellation of this Note, the Company shall execute and deliver, in lieu of this Note, a new Note executed in the same manner as this Note, in the same principal amount as the unpaid principal amount of this Note and dated the date to which interest shall have been paid on this Note or, if no interest shall have yet been so paid, dated the date of this Note.

(b) Payment. All payments under this Note shall be made in lawful tender of the United States.

(c) Waivers. The Company hereby waives notice of default, presentment or demand for payment, protest or notice of nonpayment or dishonor and all other notices or demands relative to this instrument.

(d) Usury. In the event any interest is paid on this Note which is deemed to be in excess of the then legal maximum rate, then that portion of the interest payment representing an amount in excess of the then legal maximum rate shall be deemed a payment of principal and applied against the principal of this Note.

(e) Waiver and Amendment. Any provision of this Note may be amended, waived or modified upon the written consent of the Company and the Holders of at least two-thirds of the principal amount of all then outstanding Notes issued pursuant to the Purchase Agreement.

(f) Notices. Any notice, request or other communication required or permitted hereunder shall be given in accordance with the Purchase Agreement.

(g) Expenses; Attorneys’ Fees. If action is instituted to collect this Note, the Company promises to pay all reasonable costs and expenses, including, without limitation, reasonable attorneys’ fees and costs, incurred in connection with such action.

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(h) Successors and Assigns. This Note may be assigned or transferred by the Company only with the prior written approval of the Holder. Subject to the preceding sentence, the rights and obligations of the Company and the Holder of this Note shall be binding upon and benefit the successors, assigns, heirs, administrators and transferees of the parties.

(i) Governing Law. THIS NOTE SHALL BE GOVERNED IN ALL RESPECTS BY THE LAWS OF THE STATE OF CALIFORNIA AS SUCH LAWS ARE APPLIED TO AGREEMENTS BETWEEN CALIFORNIA RESIDENTS ENTERED INTO AND TO BE PERFORMED ENTIRELY WITHIN CALIFORNIA.

(signature page follows)

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IN WITNESS WHEREOF, the Company has caused this Note to be executed by its duly authorized officer.

Capnia, Inc. – Convertible Promissory Note