WARRANT

Exhibit 4.2

WARRANT

THE SECURITIES REPRESENTED BY THIS WARRANT HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR APPLICABLE STATE SECURITIES LAWS. THE SECURITIES HAVE BEEN ACQUIRED FOR INVESTMENT AND MAY NOT BE OFFERED, SOLD, TRANSFERRED OR ASSIGNED IN THE ABSENCE OF AN EFFECTIVE REGISTRATION STATEMENT UNDER THE SECURITIES ACT OR AN OPINION OF COUNSEL, REASONABLY SATISFACTORY TO THE COMPANY, THAT REGISTRATION IS NOT REQUIRED UNDER THE SECURITIES ACT OR APPLICABLE STATE SECURITIES LAWS UNLESS SOLD PURSUANT TO RULE 144 UNDER THE SECURITIES ACT.

REGENERX BIOPHARMACEUTICALS, INC.

WARRANT TO PURCHASE COMMON STOCK

Issuance Date: December 31, 2004

THIS CERTIFIES THAT, for value received, ThinkEquity Partners L.L.C. or its registered assigns (the “Holder”) is entitled to purchase from RegeneRx Biopharmaceuticals, Inc., a Delaware corporation (the “Company”), at any time after December 31, 2004 and before the Expiration Date (defined below) at $4.05 per share (the “Exercise Price”) Eleven Thousand Five Hundred and Thirty Nine (11,539) fully paid nonassessable shares of Common Stock (defined below) (the “Warrant Shares”), all subject to adjustment and upon the terms and conditions provided herein.

Section 1. Definitions.

The following terms as used in this Warrant have the following meanings:

(a) “Business Day” means any day other than Saturday, Sunday or federal holiday.

(b) “Common Stock” means (i) the Company’s common stock, $.001 par value per share, and (ii) any capital stock into which the Common Stock is changed or any capital stock resulting from a reclassification of the Common Stock.

(c) “Engagement Letter” means letter agreement, dated September 1, 2004 between the Holder and the Company.

(d) “Exercise Price” is equal to $4.05, subject to adjustment.

(e) “Expiration Date” means the date three years after the Issuance Date or, if such date falls on a day that is not a Business Day or a day on which trading does not take place on the principal exchange or automated quotation system on which the Common Stock is traded (a “Holiday”), the next day that is not a Holiday.

(f) “Issuance Date” means December 31, 2004.

(g) “Person” means a natural person or company, or a government or any division, department or agency thereof.

(h) “Purchase Agreement” means the purchase agreement dated December 31, 2004 between the Company and various investors.

(i) “Registrable Securities” shall mean, subject to Section 5: (i) the Company securities owned by a shareholder of the Company on the date of determination; (ii) any class of stock, equity interests or other securities issued as (or issuable upon the conversion or exercise of any warrant, right or other security which is issued as) a dividend or other distribution with respect to, or in exchange by the Company generally for, or in replacement by the Company generally of, such equity interests; and (ii) any securities issued in exchange for equity interests in any merger or reorganization of the Company; provided, however, that Registrable Securities shall not include any securities which have theretofore been registered and sold pursuant to the Securities Act or which have been sold to the public pursuant to Rule 144 or any similar rule promulgated by the Commission pursuant to the Securities Act, and provided further, the Company shall have no obligation under Section 5 to register any Registrable Securities of a shareholder of the Company requesting such registration if the Company shall deliver to the requesting shareholder an opinion of counsel reasonably satisfactory to the requesting shareholder and its counsel that the registration which was requested does not require registration under the Securities Act for a sale or disposition in a single public sale and offers to remove any and all legends restricting transfer from the certificates representing such Registrable Securities. For purposes of this Agreement, a person will be deemed to be a holder of Registrable Securities whenever such person has the then existing right to acquire Registrable Securities (by conversion, purchase or otherwise) whether or not such acquisition has actually been effected.

(j) “Securities Act” means the Securities Act of 1933, as amended.

(k) “Warrant” means this Warrant and all Warrants issued in exchange, transfer or replacement thereof.

Section 2. Exercise of Warrant.

(a) This Warrant may be exercised by the Holder registered on the books of the Company, in whole or in part, at any time on any Business Day after December 31, 2004 and prior to 11:59 p.m. Eastern Time on the Expiration Date by (i) delivery of a written notice, in the form attached as Exhibit A (the “Exercise Notice”), of Holder’s election to exercise this Warrant, specifying the number of Warrant Shares to be purchased, (ii) payment to the Company of an amount equal to the Exercise Price multiplied by the number of Warrant Shares being purchased (the “Payment”) in cash or wire transfer of immediately available funds or by means of a cashless exercise pursuant to Section 3 and (iii) the surrender to a common carrier for overnight delivery to the Company, as soon as practicable following such date, of this Warrant, (or an indemnification undertaking with respect to this Warrant in the case of its loss, theft or destruction).

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The Company shall, not later than the second Business Day (the “Delivery Date”) following receipt of an Exercise Notice, the Payment and this Warrant or an indemnification (the “Exercise Documents”), arrange for its transfer agent, on or before the Delivery Date, to issue and surrender to a common carrier for overnight delivery to the address specified in the Exercise Notice, a certificate, registered in the name of the Holder, for the number of shares of Common Stock to which the Holder is entitled. Upon delivery of the Exercise Notice and the Payment, the Holder shall be deemed for all corporate purposes to have become the holder of record of the Warrant Shares with respect to which this Warrant has been exercised on the Delivery Date, irrespective of the date of delivery of the certificates evidencing the Warrant Shares.

(b) Unless the rights represented by this Warrant have expired or been fully exercised, the Company shall, as soon as practicable and in no event later than five Business Days after receipt of the Exercise Documents and at its own expense, issue a new Warrant identical in all respects to this Warrant, except it shall represent rights to purchase the number of Warrant Shares purchasable immediately prior to exercise, less the number purchased.

(c) No fractional shares of Common Stock are to be issued upon the exercise of this Warrant, but rather the number of shares of Common Stock issued shall be rounded up or down to the nearest whole number.

Section 3. Payment of Exercise Price. The Holder shall pay the Exercise Price in immediately available funds; provided, however, that the Holder may satisfy its obligation to pay the Exercise Price through a “cashless exercise,” in which the Holder shall be entitled to receive a certificate for the number of Warrant Shares equal to the quotient obtained by dividing [(A-B) (X)] by (A), where:

(A) = the average closing price for the five trading days immediately prior to (but not including) the date of such election;

(B) = the Exercise Price of the Warrants, as adjusted; and

(X) = the number of Warrant Shares issuable upon exercise of the Warrants in accordance with the terms of this Warrant.

Section 4. Covenants as to Common Stock. The Company hereby covenants and agrees as follows:

(a) This Warrant is, and any Warrants issued in substitution for or replacement of this Warrant upon issuance will be, duly authorized, executed and delivered.

(b) All Warrant Shares upon issuance will be validly issued, fully paid and nonassessable and free from all liens and charges with respect to the issue thereof.

(c) As long as this Warrant may be exercised, the Company will have authorized and reserved at least the number of shares of Common Stock needed to provide for the exercise of the rights then represented by this Warrant.

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Section 5. Piggy-Back Registrations. If at any time the Company shall determine to register for its own account or the account of others under the Securities Act (including in connection with an underwritten public offering of the Company’s Common Stock on a Form S-1, Form S-3 , Form SB-1 or Form SB-2 Registration Statement filed with the Securities and Exchange Commission under the Securities Act or a demand for registration of any shareholder of the Company) any of its equity securities, other than on Form S-8 or Form S-4 or their then equivalents relating to shares of Common Stock to be issued solely in connection with any acquisition of an entity or business or shares of Common Stock issuable in connection with stock option or other employee benefit plans, it shall send to each holder of Registrable Securities, including each holder who has the right to acquire Registrable Securities (including, if applicable, the Holder or any holder of warrant shares issued pursuant to this Warrant), written notice of such determination and if, within 15 days after receipt of such notice, such holder shall so request in writing, the Company shall use its good faith efforts to include in such registration statement all or any part of the Registrable Securities such holder requests to be registered.

If, in connection with any offering involving an underwriting of Common Stock to be issued by the Company and that is subject to the registration rights contained in this Section 5, the managing underwriter shall impose a limitation on the number of shares of such Common Stock that may be included in the registration statement because in its judgment, such limitation is necessary to effect an orderly public distribution, then the Company shall be obligated to include in such registration statement only such portion of the Registrable Securities with respect to which such holder has requested inclusion pursuant hereto as such limitation permits after the inclusion of all shares of Common Stock to be registered by the Company for its own account. Any exclusion of Registrable Securities shall be made pro rata among such holders of Registrable Securities (or their assigns) and other selling shareholders seeking to include such shares, in proportion to the number of such shares sought to be included by such holders of Registrable Securities (or their assigns) and the other selling shareholders. The obligations of the Company under this Section 5 may be waived at any time upon the written consent of holders of at least two-thirds in interest of the Registrable Securities.

Section 6. Warrant Holder Not Deemed a Shareholder. Except as specifically provided in Section 2(a), nothing contained in this Warrant shall be construed to (a) grant the Holder any rights to vote or receive dividends or be deemed the holder of shares of the Company for any purpose, (b) confer upon the Holder any of the rights of a shareholder of the Company or any right to vote, give or withhold consent to any corporate action (whether any reorganization, issue of stock, reclassification of stock, consolidation, merger, conveyance or otherwise), receive notice of meetings, receive dividends or subscription rights, or otherwise, or (c) impose any liabilities on the Holder to purchase any securities or as a shareholder of the Company, whether asserted by the Company or creditors of the Company, prior to the issuance of the Warrant Shares.

Section 7. Representations of Holder. The Holder, by the acceptance hereof, represents that it is acquiring this Warrant and the Warrant Shares for its own account for investment only and not with a view towards, or for resale in connection with, the public sale or distribution of this Warrant or the Warrant Shares, except pursuant to sales registered or

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exempted under the Securities Act. The Holder further represents, by acceptance hereof, that, as of this date, Holder is an “accredited investor” as defined in Rule 501(a)(1) of Regulation D promulgated under the Securities Act (an “Accredited Investor”). Upon exercise of this Warrant, the Holder shall, if requested by the Company, confirm in writing, in a form satisfactory to the Company, that the Warrant Shares are being acquired solely for the Holder’s own account and not as a nominee for any other party, for investment, and not with a view toward distribution or resale and that Holder is an Accredited Investor. If Holder cannot make such representations because they would be factually incorrect, it shall be a condition to Holder’s exercise of this Warrant that the Company receive such other representations as the Company considers reasonably necessary to assure the Company that the issuance of its securities upon exercise of this Warrant shall not violate any federal or state securities laws. The Company shall not be penalized or disadvantaged by a Holder’s inability to exercise this Warrant due to its inability to make the required representations in connection with the exercise of this Warrant.

Section 8. Ownership and Transfer.

(a) The Company shall maintain at its principal executive offices (or such other office or agency of the Company as it may designate by notice to the holder hereof), a register for this Warrant, in which the Company shall record the name and address of the Person in whose name this Warrant has been issued, as well as the name and address of each transferee who has acquired this Warrant in accordance with applicable law and the terms of this Warrant. The Company may treat the Person in whose name any Warrant is registered on the register as the owner and holder thereof for all purposes, notwithstanding any notice to the contrary, but in all events recognizing any transfers made in accordance with the terms of this Warrant.

(b) This Warrant may be offered, sold, transferred or assigned in compliance with the Securities Act and applicable state securities laws without the consent of the Company, except as may otherwise be required by the Purchase Agreement.

Section 9. Adjustment of Exercise Price and Number of Shares. The Exercise Price and the number of Warrant Shares shall be adjusted from time to time as follows:

(a) Stock Splits. If the Company subdivides (by any stock split, recapitalization or otherwise) its outstanding shares of Common Stock into a greater number of shares, the Exercise Price in effect immediately prior to the subdivision will be proportionately reduced and the number of Warrant Shares will be proportionately increased. If the Company combines (by combination, reverse stock split or otherwise) its outstanding shares of Common Stock into a smaller number of shares, the Exercise Price in effect immediately prior to the combination will be proportionately increased and the number of Warrant Shares will be proportionately decreased. Any adjustment under this Section shall become effective at the close of business on the date the subdivision or combination becomes effective.

(b) Stock Dividends. If the Company declares a dividend or any other distribution upon the Common Stock that is payable in shares of Common Stock or securities convertible into shares of Common Stock, the Exercise Price in effect immediately prior to the declaration of the dividend or distribution will be reduced to the quotient obtained by dividing (i) the number of shares of Common Stock outstanding immediately prior to the declaration

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multiplied by the then effective Exercise Price by (ii) the total number of shares of Common Stock outstanding immediately after the declaration.

Section 10. Purchase Rights; Reorganization, Reclassification, Consolidation, Merger or Sale.

(a) Any recapitalization, reorganization, reclassification, consolidation, merger, sale of all or substantially all of the Company’s assets to another Person or other transaction in each case that is effected in such a way that holders of Common Stock are entitled to receive (either directly or upon subsequent liquidation) stock, securities or assets with respect to or in exchange for Common Stock is referred to herein as an “Organic Change.” Upon the consummation of any (i) sale of all or substantially all of the Company’s assets to an acquiring Person or (ii) other Organic Change following which the Company is not a surviving entity, the Company will secure from the Person purchasing the assets or the successor resulting from the Organic Change (in each case, the “Acquiring Entity”) a written agreement to deliver to Holder in exchange for this Warrant, a security of the Acquiring Entity evidenced by a written instrument substantially similar in form and substance to this Warrant and reasonably satisfactory to the Holder. Prior to the consummation of any other Organic Change, the Company shall make appropriate provision to insure that Holder will thereafter have the right to acquire and receive in lieu of the shares of Common Stock immediately theretofore acquirable and receivable upon the exercise of this Warrant, such shares of stock, securities or assets that would have been issued or payable in the Organic Change with respect to or in exchange for the number of Warrant Shares that would have been acquirable as of the date of the Organic Change.

Section 11. Lost, Stolen, Mutilated or Destroyed Warrant. If this Warrant is lost, stolen, mutilated or destroyed, the Company shall promptly, on receipt of an indemnification undertaking reasonably satisfactory to the Company (or, in the case of a mutilated Warrant, the Warrant), issue a new Warrant of like denomination and tenor as this Warrant so lost, stolen, mutilated or destroyed.

Section 12. Notice. Any notices, consents, waivers or other communications required or permitted to be given under the terms of this Warrant must be in writing and will be deemed to have been delivered: (i) upon receipt, when delivered personally; (ii) upon receipt, when sent by fax transmittal (provided confirmation of transmission is mechanically or electronically generated and kept on file by the sending party); or (iii) one Business Day after deposit with a nationally recognized overnight delivery service, in each case properly addressed to the party to receive the same. The addresses and fax numbers for communications shall be:

If to the Company:

RegeneRx Biopharmaceuticals, Inc.

3 Bethesda Metro Center, Suite 700

Bethesda, Maryland 20814

Fax: (301) 961-1991

Attention: President, Chief Executive Officer and Principal Financial Officer

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With a copy to:

Patton Boggs LLP

2550 M Street, N.W.

Washington, DC 20037

Fax: (202) 457-6315

Attention: Philip G. Feigen, Esq.

If to the Holder:

ThinkEquity Partners L.L.C.

600 Montgomery Street

8th Floor

San Francisco, California 94111

Each party shall provide five days’ prior written notice to the other party of any change in address or fax number. Written confirmation of receipt (A) given by the recipient of any notice, consent, waiver or other communication, (B) mechanically or electronically generated by the sender’s fax machine containing the time, date, recipient fax number and an image of the first page of the transmission, or (C) provided by a nationally recognized overnight delivery service, shall be rebuttable evidence of receipt.

Section 13. Remedies, Other Obligations, Breaches and Injunctive Relief. The remedies provided in this Warrant shall be cumulative and in addition to all other remedies available under this Warrant, the Purchase Agreement and the Engagement Letter, at law or in equity (including a decree of specific performance and/or other injunctive relief), and nothing herein shall limit the right of the Holder to pursue actual damages for any failure by the Company to comply with the terms of this Warrant. The Company acknowledges that a breach of its obligations hereunder will cause irreparable harm to the Holder and that the remedy at law for any such breach may be inadequate. The Company therefore agrees that, in the event of any such breach or threatened breach, the Holder shall be entitled, in addition to all other available remedies, to an injunction restraining any breach, without the necessity of showing economic loss and without any bond or other security being required.

Section 14. Amendment and Waiver. Except as otherwise provided herein, this Warrant may not be modified or amended except pursuant to an instrument in writing signed by the Company and the Holder. No provision hereunder may be waived other than in a written instrument executed by the waiving party.

Section 15. Governing Law. This Warrant shall be construed and enforced in accordance with, and all questions concerning the construction, validity, interpretation and performance of this Warrant shall be governed by, the internal laws of the State of California, without giving effect to any choice of law or conflict of law provision or rule (whether of the State of California or any other jurisdictions) that would cause the application of the laws of any jurisdictions other than the State of California.

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Section 16. Restrictive Legends. At all times this Warrant and until such time as the Registration Statement (as defined in the Purchase Agreement) has been declared effective or the Warrant Shares may be sold pursuant to Rule 144(k) under the Securities Act without any restriction as to the number of securities that can then be immediately sold, certificates for any Warrant Shares will, in addition to any legend required under applicable securities law, bear a restrictive legend substantially in the form first set forth above.

[Signature Page Follows]

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IN WITNESS WHEREOF, the Company has caused this Warrant to be signed as of December 31, 2004.

Exhibit A To Warrant

REGENERX BIOPHARMACEUTICALS, INC.

EXERCISE NOTICE

TO BE EXECUTED BY THE REGISTERED HOLDER

TO EXERCISE THIS WARRANT

The undersigned holder hereby exercises the right to purchase                                  shares of Common Stock (“Warrant Shares”) of RegeneRx Biopharmaceuticals, Inc., a Delaware corporation (the “Company”), evidenced by the attached Warrant (the “Warrant”). Capitalized terms used herein and not otherwise defined shall have the respective meanings set forth in the Warrant.

1. Payment of Exercise Price (check applicable box).

[    ] Payment in the sum of $                 [is enclosed] [has been wire transferred to the Company at the following account:                     ] in accordance with the terms of the Warrant.

[    ] The cancellation of such number of Warrant Shares as is necessary, in accordance with the formula set forth in subsection 2(c) of the Warrant, to exercise this Warrant with respect to the maximum number of Warrant Shares purchasable pursuant to the cashless exercise procedure set forth in subsection 2(c).

2. Delivery of Warrant Shares. The Company shall deliver the Warrant Shares in the name of the undersigned or in such other name as is specified below in accordance with the terms of the Warrant at the following address:

3. Accredited Investor. The undersigned is an “accredited investor” as defined in Regulation D promulgated under the Securities Act of 1933, as amended.

Date:                          ,                 

ACKNOWLEDGMENT

The Company hereby acknowledges this Exercise Notice and hereby directs                 . to issue the above indicated number of shares of Common Stock in accordance with the Transfer Agent Instructions dated                 , 200_ from the Company and acknowledged and agreed to by                     .