HORIZON PHARMA, INC. WARRANT TO PURCHASE COMMON STOCK

Exhibit 4.1

THIS WARRANT AND THE UNDERLYING SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED OR THE SECURITIES LAWS OF ANY STATE OF THE UNITED STATES. THE SECURITIES MAY NOT BE SOLD, OFFERED FOR SALE, PLEDGED, HYPOTHECATED, TRANSFERRED OR ASSIGNED IN THE ABSENCE OF AN EFFECTIVE REGISTRATION STATEMENT FOR THE SECURITIES UNDER APPLICABLE SECURITIES LAWS OR UNLESS OFFERED, SOLD, PLEDGED, HYPOTHECATED OR TRANSFERRED PURSUANT TO AN AVAILABLE EXEMPTION FROM THE REGISTRATION REQUIREMENTS OF THOSE LAWS. THE COMPANY SHALL BE ENTITLED TO REQUIRE AN OPINION OF COUNSEL SATISFACTORY TO THE COMPANY THAT SUCH REGISTRATION IS NOT REQUIRED TO THE EXTENT THAT AN OPINION IS REQUIRED PURSUANT TO THE AGREEMENT UNDER WHICH THE SECURITIES WERE ISSUED.

HORIZON PHARMA, INC.

WARRANT TO PURCHASE COMMON STOCK

March 2, 2012

Void After March 2, 2017

THIS CERTIFIES THAT, for value received, [            ], with its principal office at [                    ], or permitted assigns (the “Holder”), is entitled to subscribe for and purchase at the Exercise Price (defined below) from Horizon Pharma, Inc., a Delaware corporation, with its principal office at 520 Lake Cook Road, Suite 520, Deerfield, Illinois 60015 (the “Company”) up to [            ] shares of the Common Stock of the Company (the “Common Stock”), subject to adjustment as provided herein. This Warrant is one of a series of Warrants being issued pursuant to the terms of the Securities Purchase Agreement, dated February 28, 2012, by and among the Company and the original Holder of this Warrant and the other parties named therein (the “Purchase Agreement”). Capitalized terms not otherwise defined herein shall have the respective meanings ascribed to such terms in the Purchase Agreement.

1.    DEFINITIONS. As used herein, the following terms shall have the following respective meanings:

(a) “Exercise Period” shall mean the period commencing on March 2, 2012 and ending March 2, 2017, unless sooner terminated as provided below.

(b) “Exercise Price” shall mean $4.308 per share, subject to adjustment pursuant to Section 5 below.

(c) “Exercise Shares” shall mean the shares of the Company’s Common Stock issued or issuable upon exercise of this Warrant, subject to adjustment pursuant to the terms herein, including but not limited to adjustment pursuant to Section 5 below.

2.    EXERCISE OF WARRANT.

2.1 Method of Exercise. The rights represented by this Warrant may be exercised in whole or in part at any time during the Exercise Period, by delivery of the following to the Company at its address set forth above (or at such other address as it may designate by notice in writing to the Holder):

(a) An executed Notice of Exercise in the form attached hereto; and

(b) Payment of the Exercise Price either (i) in cash or by check or wire transfer of immediately available funds, or (ii) pursuant to a Cashless Exercise, as described below.

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2.2 Cashless Exercise. Notwithstanding any provisions herein to the contrary, if, at any time during the Exercise Period, the Current Market Price (as defined below) of one share of Common Stock is greater than the Exercise Price (at the date of calculation as set forth below), in lieu of exercising this Warrant by payment of cash, the Holder may exercise this Warrant by a cashless exercise by surrender of this Warrant at the principal office of the Company together with the properly endorsed Notice of Exercise and the Company shall issue to the Holder a number of shares of Common Stock computed using the following formula:

“Current Market Price” means on any particular date:

(a) if the Common Stock is traded on The Nasdaq Global Market or The Nasdaq Capital Market, the closing price of the Common Stock of the Company on such market on the Trading Day prior to the applicable date of valuation;

(b) if the Common Stock is traded on any registered national stock exchange but is not traded on The Nasdaq Global Market or The Nasdaq Capital Market, the closing price of the Common Stock of the Company on such exchange on the Trading Day prior to the applicable date of valuation;

(c) if the Common Stock is traded over-the-counter, but not on The Nasdaq Global Market, The Nasdaq Capital Market or a registered national stock exchange, the closing bid price of the Common Stock of the Company on the day prior to the applicable date of valuation; and

(d) if there is no active public market for the Common Stock, the value thereof, as determined in good faith by the Board of Directors of the Company upon due consideration of the proposed determination thereof by the Holder.

2.3 Partial Exercise. If this Warrant is exercised in part only, the Company shall, upon surrender of this Warrant, execute and deliver, within 10 days of the date of exercise, a new Warrant evidencing the rights of the Holder, or such other person as shall be designated in the Notice of Exercise, to purchase the balance of the Exercise Shares purchasable hereunder. In no event shall this Warrant be exercised for a fractional Exercise Share, and the Company shall not distribute a Warrant exercisable for a fractional Exercise Share. Fractional shares shall be treated as provided in Section 6 hereof.

2.4 No Settlement for Cash. Except as provided in Section 5.3, this Warrant cannot be settled with the Company for cash.

2.5 [Reserved.]

2.6 Delivery of Shares. Exercise Shares acquired hereunder shall be delivered to the Holder within three Trading Days after the date on which this Warrant shall have been validly exercised. Such Exercise Shares shall be in certificated form and bear an appropriate restrictive legend unless otherwise required under the terms of the Purchase Agreement. The person in whose name any Exercise Shares are to be issued upon exercise of this Warrant shall be deemed to have become the holder of record of such shares on the date on which this Warrant was validly exercised, irrespective of the date of issuance of the shares of Common Stock, except that, if the date of such valid exercise is a date when the stock transfer books of the Company are closed, such person shall be deemed to have become the holder of such shares at the close of business on the next succeeding date on which the stock transfer books are open.

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2.7 Failure to Deliver Exercise Shares. If the Company fails to deliver to the Holder Exercise Shares pursuant to Section 2.6 by noon, Eastern Standard Time, on the third Trading Day after the date of a valid exercise of this Warrant, then the Company shall,

(a) at the option of the Holder, either,

(i) rescind such exercise and reinstate the portion of the Warrant and equivalent number of Exercise Shares for which such exercise was not honored, in lieu of delivering such Exercise Shares; or

(ii) deliver to the Holder the Exercise Shares that would have been issued had the Company timely complied with its exercise and delivery obligations hereunder; and

(b) if after noon, Eastern Standard Time, on the third Trading Day the Holder or the Holder’s brokerage firm purchases shares of the same class and series as the Exercise Shares to deliver in satisfaction of a sale by the Holder of the Exercise Shares which the Holder anticipated receiving upon such exercise (a “Buy-In”), pay in cash to the Holder the amount by which,

(i) the Holder’s total purchase price (including brokerage commissions, if any) for the shares so purchased, exceeds

(ii) the amount obtained by multiplying (1) the number of Exercise Shares that the Company was required to deliver to the Holder in connection with the exercise, by (2) the price at which the sell order giving rise to such purchase obligation was executed.

The Holder shall provide the Company prompt written notice indicating the amounts payable to the Holder in respect of any Buy-In, together with applicable confirmations and other evidence reasonably requested by the Company (a “Buy-In Notice”). The Company shall pay the amounts payable to the Holder in respect of any Buy-In within three Trading Days after the Company’s receipt of the Buy-In Notice.

3.    COVENANTS OF THE COMPANY.

3.1 Covenants as to Exercise Shares. The Company covenants and agrees that it will at all times during the Exercise Period, have authorized and reserved, free from preemptive rights, a sufficient number of shares of its Common Stock to provide for the exercise of the rights represented by this Warrant. All Exercise Shares will, upon issuance, be validly issued and outstanding, fully paid and nonassessable, and free from all taxes, liens and charges with respect to the issuance thereof. If at any time during the Exercise Period the number of authorized but unissued shares of Common Stock shall not be sufficient to permit exercise of this Warrant, the Company will take such corporate action as may, in the opinion of its counsel, be necessary to increase its authorized but unissued shares of Common Stock (or other securities as provided herein) to such number of shares as shall be sufficient for such purposes.

3.2 No Impairment. Except and to the extent as waived or consented to by the Holder, the Company will not, by amendment of its Certificate of Incorporation (as such may be amended from time to time), or through any means, avoid or seek to avoid the observance or performance of any of the terms to be observed or performed hereunder by the Company, but will at all times in good faith assist in the carrying out of all the provisions of this Warrant and in the taking of all such action as may be necessary or appropriate in order to protect the exercise rights of the Holder against impairment.

3.3 Notices of Record Date. In the event of any taking by the Company of a record of the holders of any class of securities for the purpose of determining the holders thereof who are entitled to (a) receive any dividend (other than a Common Stock dividend subject to Section 5.1) or (b) vote with respect to a capital reorganization of the Company, a reclassification, recapitalization or exchange of the capital stock of the Company, a consolidation or merger of the Company

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with, or any sale, transfer or other disposition of all or substantially all the property, assets or business of the Company to, another Person, or a voluntary dissolution, liquidation or winding up of the Company, then the Company shall mail to the Holder, at least ten Trading Days prior to such record date, a notice specifying the date on which any such record is to be taken for the purpose of such dividend or vote.

3.4 Automatic Exercise. Notwithstanding anything herein to the contrary other than Section 2.5, to the extent this Warrant remains exercisable and is exercisable pursuant to Section 2.2, this Warrant shall be deemed to be fully exercised pursuant to Section 2.2, without the need for any action by the Holder or the Company, immediately prior to the end of the Exercise Period; provided, however, that notwithstanding any other provision hereof or in the Purchase Agreement, the Company may delay the delivery of Exercise Shares pursuant to such an automatic exercise until the Holder delivers to the Company a certification substantially in the form of Section 3 of the Notice of Exercise attached hereto.

4.    REPRESENTATIONS OF HOLDER.

4.1 Acquisition of Warrant for Personal Account. The Holder represents and warrants that it is acquiring the Warrant and the Exercise Shares solely for its account for investment and not with a present view toward the public distribution of said Warrant or Exercise Shares or any part thereof and has no intention of selling or distributing said Warrant or Exercise Shares or any arrangement or understanding with any other persons regarding the sale or distribution of said Warrant or, except in accordance with the provisions of Article 6 of the Purchase Agreement, the Exercise Shares, and except as would not result in a violation of the Securities Act. The Holder will not, directly or indirectly, offer, sell, pledge, transfer or otherwise dispose of (or solicit any offers to buy, purchase or otherwise acquire or take a pledge of) the Warrant except in accordance with the Securities Act and will not, directly or indirectly, offer, sell, pledge, transfer or otherwise dispose of (or solicit any offers to buy, purchase or otherwise acquire or take a pledge of) the Exercise Shares except in accordance with the provisions of Article 6 of the Purchase Agreement or pursuant to and in accordance with the Securities Act.

4.2 Securities Are Not Registered.

(a) The Holder understands that the offer and sale of the Warrant or the Exercise Shares have not been registered under the Securities Act on the basis that no distribution or public offering of the stock of the Company is to be effected. The Holder realizes that the basis for the exemption may not be present if, notwithstanding its representations, the Holder has a present intention of acquiring the securities for a fixed or determinable period in the future, selling (in connection with a distribution or otherwise), granting any participation in, or otherwise distributing the securities. The Holder has no such present intention.

(b) The Holder recognizes that the Warrant and the Exercise Shares must be held indefinitely unless they are subsequently registered under the Securities Act or an exemption from such registration is available. The Holder recognizes that the Company has no obligation to register the Warrant or, except as provided in the Purchase Agreement, the Exercise Shares.

4.3 Disposition of Warrant and Exercise Shares.

(a) The Holder further agrees not to make any disposition of all or any part of the Warrant or Exercise Shares in any event unless and until:

(i) The Company shall have received a letter secured by the Holder from the SEC stating that no action will be recommended to the SEC with respect to the proposed disposition;

(ii) There is then in effect a registration statement under the Securities Act covering such proposed disposition and such disposition is made in accordance with said registration statement; or

(iii) The Holder shall have notified the Company of the proposed disposition and shall have furnished the Company with a detailed statement of the circumstances surrounding the proposed disposition, and if reasonably requested by the Company, the Holder shall have furnished the Company with an opinion of counsel, reasonably

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satisfactory to the Company, for the Holder to the effect that such disposition will not require registration of such Warrant or Exercise Shares under the Securities Act or any applicable state securities laws; provided, that no opinion shall be required for any disposition made or to be made in accordance with the provisions of Rule 144.

(b) The Holder understands and agrees that all certificates evidencing the Exercise Shares to be issued to the Holder may bear a legend in substantially the following form; provided, that such legend shall be removed (or such Exercise Shares shall be issued without such legend upon exercise of this Warrant) as required pursuant to Section 3.8(b) of the Purchase Agreement:

THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR THE SECURITIES LAWS OF ANY STATE OF THE UNITED STATES. THE SECURITIES MAY NOT BE SOLD, OFFERED FOR SALE, PLEDGED, HYPOTHECATED, TRANSFERRED OR ASSIGNED IN THE ABSENCE OF AN EFFECTIVE REGISTRATION STATEMENT FOR THE SECURITIES UNDER APPLICABLE SECURITIES LAWS, OR UNLESS OFFERED, SOLD, PLEDGED, HYPOTHECATED OR TRANSFERRED PURSUANT TO AN AVAILABLE EXEMPTION FROM THE REGISTRATION REQUIREMENTS OF THOSE LAWS. THE COMPANY SHALL BE ENTITLED TO REQUIRE AN OPINION OF COUNSEL SATISFACTORY TO THE COMPANY THAT SUCH REGISTRATION IS NOT REQUIRED TO THE EXTENT THAT SUCH OPINION IS REQUIRED PURSUANT TO THAT CERTAIN SECURITIES PURCHASE AGREEMENT UNDER WHICH THE SECURITIES WERE ISSUED.

5.    CERTAIN ADJUSTMENTS.

5.1 Subdivisions, Combinations and Other Issuances. In the event the Company pays a dividend in Common Stock or makes a distribution in Common Stock to holders of its outstanding Common Stock; subdivides its outstanding Common Stock into a greater number of shares; combines its outstanding Common Stock into a smaller number of shares; or issues any shares of its capital stock in a reclassification of the Common Stock, the number and class of shares available under the Warrant in the aggregate and the Exercise Price shall be correspondingly adjusted to give the Holder of the Warrant, on exercise for the same aggregate Exercise Price, the total number, class, and kind of shares as the Holder would have owned had the Warrant been exercised prior to the event and had the Holder continued to hold such shares until after the event requiring adjustment. The form of this Warrant need not be changed because of any adjustment in the number, class, and kind of shares subject to this Warrant. The Company shall promptly provide a certificate from its Chief Financial Officer notifying the Holder in writing of any adjustment in the Exercise Price and/or the total number, class, and kind of shares issuable upon exercise of this Warrant, which certificate shall specify the Exercise Price and number, class and kind of shares under this Warrant after giving effect to such adjustment.

5.2 Pro Rata Distributions. If the Company, at any time while this Warrant is outstanding, distributes to holders of Common Stock (i) evidences of its indebtedness, (ii) any security (other than a distribution of Common Stock subject to Section 5.1), (iii) rights or warrants to subscribe for or purchase any security, or (iv) any other asset (in each case, “Distributed Property”), then in each such case the Holder shall be entitled upon exercise of this Warrant for the purchase of any or all of the Exercise Shares, to receive the amount of Distributed Property which would have been payable to the Holder had such Holder been the holder of such Exercise Shares on the record date for the determination of stockholders entitled to such Distributed Property. The Company will at all times set aside and keep available for distribution to the Holder upon exercise of this Warrant a portion of the Distributed Property to satisfy the distribution to which such Holder is entitled pursuant to the preceding sentence. The Company shall promptly provide a certificate from its Chief Financial Officer notifying the Holder in writing of any distributions to which this Section 5.2 applies.

5.3 Fundamental Transactions.

(a) If the Company consummates (i) a merger or consolidation with or into another entity, as a result of which the holders of the Company’s outstanding voting securities as of immediately prior to such merger or consolidation hold less than a majority of the outstanding voting securities of the surviving or successor entity as of immediately after such merger or consolidation or (ii) a sale, transfer or other disposition of all or substantially all its property, assets or business to another person or entity (any such transaction being hereinafter referred to as a “Fundamental Transaction”), then the

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Company shall ensure that lawful and adequate provision shall be made whereby the Holder shall thereafter have the right to purchase and receive upon the basis and upon the terms and conditions herein specified and in lieu of the Exercise Shares immediately theretofore issuable upon exercise of this Warrant, such shares of stock, securities or assets as would have been issuable or payable with respect to or in exchange for a number of Exercise Shares equal to the number of Exercise Shares immediately theretofore issuable upon exercise of this Warrant, had such Fundamental Transaction not taken place. The provisions of this Section 5.3 shall similarly apply to successive consolidations, mergers, sales, transfers or other dispositions.

(b) Notwithstanding the foregoing, if any Fundamental Transaction (i) constitutes or results in a “going private” transaction as defined in Rule 13e-3 under the Exchange Act or (ii) pursuant to the operation of Section 5.3(a), results in this Warrant being exercisable, in whole or in part, for securities of a Person not traded on an Eligible Market, then the Company (or any such successor or surviving entity) will redeem this Warrant from the Holder for a purchase price, payable in cash on the closing date of such Fundamental Transaction, equal to the Black Scholes Value of the remaining unexercised portion of this Warrant on the closing date of such Fundamental Transaction. “Black Scholes Value” means the value of this Warrant based on the Black Scholes Option Pricing Model obtained from the “OV” function on Bloomberg determined as of the day immediately following the public announcement of the applicable Fundamental Transaction and reflecting (i) a risk-free interest rate corresponding to the U.S. Treasury rate for a period equal to the remaining term of this Warrant as of such date and (ii) an expected volatility equal to the 30-day volatility obtained from the HVT function on Bloomberg as of the Trading Day immediately prior to such day.

6.    FRACTIONAL SHARES. No fractional shares shall be issued upon the exercise of this Warrant as a consequence of any adjustment pursuant hereto. All Exercise Shares (including fractions) issuable upon exercise of this Warrant may be aggregated for purposes of determining whether the exercise would result in the issuance of any fractional share. If, after aggregation, the exercise would result in the issuance of a fractional share, the Company shall, in lieu of issuance of any fractional share, pay the Holder otherwise entitled to such fraction a sum in cash equal to the product resulting from multiplying the then current fair market value of an Exercise Share by such fraction.

7.    NO STOCKHOLDER RIGHTS. This Warrant in and of itself shall not entitle the Holder to any voting rights or other rights as a stockholder of the Company.

8.    TRANSFER OF WARRANT. Subject to applicable laws and compliance with Section 4.3 hereof, this Warrant and all rights hereunder are transferable, by the Holder in person or by duly authorized attorney, upon delivery of this Warrant and the form of assignment attached hereto to any transferee designated by Holder. The transferee shall sign an investment letter in form and substance satisfactory to the Company.

9.    LOST, STOLEN, MUTILATED OR DESTROYED WARRANT. If this Warrant is lost, stolen, mutilated or destroyed, the Company may, on such terms as to indemnity or otherwise as it may reasonably impose (which shall, in the case of a mutilated Warrant, include the surrender thereof), issue a new Warrant of like denomination and tenor as the Warrant so lost, stolen, mutilated or destroyed. Any such new Warrant shall constitute an original contractual obligation of the Company, whether or not the allegedly lost, stolen, mutilated or destroyed Warrant shall be at any time enforceable by anyone.

10.    MODIFICATIONS AND WAIVER. This Warrant and any provision hereof may be waived, modified or amended only by an instrument in writing signed by the Company and the Holder.

11.    NOTICES, ETC. All notices required or permitted hereunder shall be in writing and shall be deemed effectively given: (a) upon personal delivery to the party to be notified, (b) when sent by confirmed email, telex or facsimile if sent during normal business hours of the recipient, if not, then on the next business day, (c) five days after having been sent by registered or certified mail, return receipt requested, postage prepaid, or (d) one business day after deposit with a nationally recognized overnight courier, specifying next day delivery, with written verification of receipt. All communications shall be sent to the Company at the address listed on the signature page and to the Holders at the addresses on the Company records, or at such other address as the Company or Holder may designate by ten days’ advance written notice to the other party hereto.

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12.    ACCEPTANCE. Receipt of this Warrant by the Holder shall constitute acceptance of and agreement to all of the terms and conditions contained herein.

13.    GOVERNING LAW. This Warrant and all rights, obligations and liabilities hereunder shall be governed by the laws of the State of New York without regard to the principles of conflict of laws.

14.    DESCRIPTIVE HEADINGS. The descriptive headings of the several paragraphs of this Warrant are inserted for convenience only and do not constitute a part of this Warrant. The language in this Warrant shall be construed as to its fair meaning without regard to which party drafted this Warrant.

15.    SEVERABILITY. The invalidity or unenforceability of any provision of this Warrant in any jurisdiction shall not affect the validity or enforceability of such provision in any other jurisdiction, or affect any other provision of this Warrant, which shall remain in full force and effect.

16.    ENTIRE AGREEMENT. This Warrant constitutes the entire agreement between the parties pertaining to the subject matter contained in it and supersedes all prior and contemporaneous agreements, representations, and undertakings of the parties, whether oral or written, with respect to such subject matter.

[Signature Page Follows]

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IN WITNESS WHEREOF, the Company has caused this Warrant to be executed by its duly authorized officer as of March 2, 2012.

NOTICE OF EXERCISE

TO: HORIZON PHARMA, INC.

(1) The undersigned hereby elects to (check one box only):

¨ purchase                      shares of the Common Stock of Horizon Pharma, Inc. (the “Company”) pursuant to the terms of the attached Warrant, and tenders herewith payment of the exercise price in full for such shares.

¨ purchase the number of shares of Common Stock of the Company by cashless exercise pursuant to the terms of the Warrant as shall be issuable upon cashless exercise of the portion of the Warrant relating to                      shares.

(2) Please issue a certificate or certificates representing said shares of Common Stock in the name of the undersigned or in such other name as is specified below:

(3) The undersigned represents that (i) the aforesaid shares of Common Stock are being acquired for the account of the undersigned for investment and not with a view to, or for resale in connection with, the distribution thereof and that the undersigned has no present intention of distributing or reselling such shares; (ii) the undersigned is aware of the Company’s business affairs and financial condition and has acquired sufficient information about the Company to reach an informed and knowledgeable decision regarding its investment in the Company; (iii) the undersigned is experienced in making investments of this type and has such knowledge and background in financial and business matters that the undersigned is capable of evaluating the merits and risks of this investment and protecting the undersigned’s own interests; (iv) the undersigned understands that the shares of Common Stock issuable upon exercise of this Warrant have not been registered under the Securities Act of 1933, as amended (the “Securities Act”), by reason of a specific exemption from the registration provisions of the Securities Act, which exemption depends upon, among other things, the bona fide nature of the investment intent as expressed herein, and, because such securities have not been registered under the Securities Act, they must be held indefinitely unless subsequently registered under the Securities Act or an exemption from such registration is available; and (v) the undersigned agrees not to make any disposition of all or any part of the aforesaid shares of Common Stock unless and until there is then in effect a registration statement under the Securities Act covering such proposed disposition and such disposition is made in accordance with said registration statement, or the undersigned has furnished the Company with an opinion of counsel, reasonably satisfactory to the Company, to the effect that such disposition is not required to be registered pursuant to the Securities Act or any applicable state securities laws; provided, that no opinion shall be required for any disposition made or to be made in accordance with the provisions of Rule 144.

ASSIGNMENT FORM

(To assign the foregoing Warrant, subject to compliance with section 4.3 hereof, execute this form and supply required information. Do not use this form to purchase shares.)

FOR VALUE RECEIVED, the foregoing Warrant and all rights evidenced thereby are hereby assigned to

NOTE: The signature to this Assignment Form must correspond with the name as it appears on the face of the Warrant, without alteration or enlargement or any change whatever. Officers of corporations and those acting in a fiduciary or other representative capacity should file proper evidence of authority to assign the foregoing Warrant.