POZEN INC.

EXHIBIT 10.4

POZEN INC.

2000 EQUITY COMPENSATION PLAN

RESTRICTED STOCK UNIT AGREEMENT

This RESTRICTED STOCK UNIT AGREEMENT (the “Agreement”), dated as of May 4, 2004 (the “Date of Grant”), is delivered by POZEN Inc. (“POZEN”), to John R. Plachetka (the “Grantee”).

RECITALS

The POZEN Inc. 2000 Equity Compensation Plan, as amended (the “Plan”) provides for the grant of stock-based awards with respect to shares of common stock, par value $0.001 per share, of POZEN (the “Common Stock”), in accordance with the terms and conditions of the Plan. The Compensation Committee of the Board of Directors of POZEN (the “Committee”) has decided to make a stock-based award in the form of a grant of stock units, subject to the terms and conditions set forth in this Agreement and the Plan, as an inducement for the Grantee to promote the best interests of POZEN and its stockholders. The Grantee may receive a copy of the Plan by contacting the Department of Finance and Administration at POZEN.

NOW, THEREFORE, the parties to this Agreement, intending to be legally bound hereby, agree as follows:

1. Grant of Restricted Units. Subject to the terms and conditions set forth in this Agreement and the Plan, POZEN hereby grants to the Grantee 98,135 stock units (the “Restricted Units”) under the Plan. The Grantee accepts the Restricted Units and agrees to be bound by the terms and conditions of this Agreement and the Plan with respect to the Restricted Units.

2. Restricted Unit Account. Restricted Units represent hypothetical shares of Common Stock, and not actual shares of stock. POZEN shall establish and maintain a Restricted Unit account, as a bookkeeping account on its records, for the Grantee and shall record in such account the number of Restricted Units granted to the Grantee. No shares of stock shall be issued to the Grantee at the time the grant is made, and the Grantee shall not be, nor have any of the rights or privileges of, a stockholder of POZEN with respect to any Restricted Units recorded in the account. The Grantee shall not have the right to receive any dividends or other distributions with respect to hypothetical shares of stock recorded in the Restricted Unit account; provided, however, that the Committee may appropriately adjust the number and kind of Restricted Units in the event of a stock split, stock dividend or other change in capitalization of POZEN, as described in the Plan. The Grantee shall not have any interest in any fund or specific assets of POZEN by reason of this award or the Restricted Unit account established for the Grantee.

3. Lapse of Restrictions.

(a) The Restricted Units shall be subject to forfeiture until the restrictions on the Restricted Units lapse. The restrictions on the Restricted Units shall lapse, and the Restricted Units shall become vested, according to the following schedule, if the Grantee continues to be employed by, or provide service to, the Company (as defined in Section 5(e)(v)(A) of the Plan) from the Date of Grant until the applicable vesting date:

The lapse of restrictions on the Restricted Units shall be cumulative, but shall not exceed 100% of the Restricted Units. If the foregoing schedule would produce fractional Units, the number of Restricted Units on which the restrictions lapse shall be rounded down to the nearest whole Unit, with all restrictions lapsing on the third anniversary of the Date of Grant if the Grantee is then employed by, or providing service to, the Company.

(b) When the restrictions on Restricted Units lapse as described above, the Restricted Units shall be vested and shall no longer be subject to forfeiture. The Restricted Units shall continue to be credited to an account on the Company’s records (the “Restricted Unit Account”). When the Grantee ceases to be employed by, or provide service to, the Company, the Company shall pay to the Grantee whole shares of Common Stock equal to the number of vested whole Restricted Units then credited to the Restricted Unit Account, as described in Paragraph 5 below. Any vested amounts representing partial shares shall be paid in cash.

4. Termination of Restricted Units. If the Grantee ceases to be employed by, or provide service to, the Company for any reason before the restrictions on all the Restricted Units lapse, any Restricted Units for which the restrictions have not lapsed according to the vesting schedule above shall automatically terminate and shall be forfeited as of the date of the Grantee’s termination of employment or service. No payment shall be made with respect to any Restricted Units that terminate as described in this Paragraph 4.

5. Payment of Restricted Units.

(a) As soon as practicable after the Grantee ceases to be employed by, or provide service to, the Company, POZEN will issue to the Grantee one share of Common Stock for each whole vested Restricted Unit credited to the Restricted Unit Account, subject to satisfaction of the Grantee’s tax withholding obligations as described below. Any vested amounts representing partial shares shall be paid in cash.

(b) All obligations of POZEN under this Agreement shall be subject to the rights of the Company as set forth in the Plan to withhold amounts required to be withheld for applicable taxes. Subject to Committee approval, the Grantee may elect to satisfy any tax withholding

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obligation of the Company with respect to the Restricted Units by having shares of Common Stock withheld up to an amount that does not exceed the minimum applicable withholding tax rate for federal (including FICA), state, and local tax liabilities.

(c) The obligation of POZEN to deliver shares hereunder shall also be subject to the condition that if at any time the Committee shall determine in its discretion that the listing, registration or qualification of the shares of Common Stock upon any securities exchange or under any state or federal law, or the consent or approval of any governmental regulatory body, is necessary or desirable as a condition of, or in connection with, the issue of shares, the shares may not be issued in whole or in part unless such listing, registration, qualification, consent or approval shall have been effected or obtained free of any conditions not acceptable to the Committee. The issuance of shares of Common Stock to the Grantee pursuant to this Agreement is subject to any applicable taxes and other laws or regulations of the United States or of any state having jurisdiction thereof.

(d) The Grantee agrees to be bound by the Company’s policies regarding transfer of shares of Common Stock and understands that there may be certain times during the year in which the Grantee will be prohibited from selling, transferring, pledging, donating, assigning, mortgaging, hypothetically or encumbering shares.

6. Change of Control. The provisions of the Plan applicable to a Change of Control (as defined in the Plan) shall apply to the Restricted Units, and, in the event of a Change of Control, the Committee may take such actions as it deems appropriate pursuant to the Plan.

7. Grant Subject to Plan Provisions. This grant is made pursuant to the Plan, the terms of which are incorporated herein by reference, and in all respects shall be interpreted in accordance with the Plan. The grant and payment of the Restricted Units are subject to interpretations, regulations and determinations concerning the Plan established from time to time by the Committee in accordance with the provisions of the Plan, including, but not limited to, provisions pertaining to (i) rights and obligations with respect to withholding taxes, (ii) the registration, qualification or listing of the shares issued under the Plan, (iii) changes in capitalization of POZEN and (iv) other requirements of applicable law. The Committee shall have the authority to interpret and construe the Restricted Units pursuant to the terms of the Plan, and its decisions shall be conclusive as to any questions arising hereunder.

8. No Employment or Other Rights. The grant of the Restricted Units shall not confer upon the Grantee any right to be retained by or in the employ or service of the Company and shall not interfere in any way with the right of the Company to terminate the Grantee’s employment or service at any time. The right of the Company to terminate at will the Grantee’s employment or service at any time for any reason is specifically reserved.

9. No Stockholder Rights. Neither the Grantee, nor any person entitled to receive payment in the event of the Grantee’s death, shall have any of the rights and privileges of a stockholder with respect to shares of Common Stock, until certificates for shares have been issued upon payment of Restricted Units.

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10. Assignment and Transfers. Except as the Committee may otherwise permit pursuant to the Plan, the rights and interests of the Grantee under this Agreement may not be sold, assigned, encumbered or otherwise transferred except, in the event of the death of the Grantee, by will or by the laws of descent and distribution. In the event of any attempt by the Grantee to alienate, assign, pledge, hypothecate, or otherwise dispose of the Restricted Units or any right hereunder, except as provided for in this Agreement, or in the event of the levy or any attachment, execution or similar process upon the rights or interests hereby conferred, POZEN may terminate the Restricted Units by notice to the Grantee, and the Restricted Units and all rights hereunder shall thereupon become null and void. The rights and protections of POZEN hereunder shall extend to any successors or assigns of POZEN and to POZEN’s parents, subsidiaries, and affiliates. This Agreement may be assigned by POZEN without the Grantee’s consent.

11. Unfunded Arrangement. The Grantee’s rights to receive payments under this Agreement shall be no greater than the right of an unsecured general creditor of the Company. All payments shall be made from the general assets of the Company, and no special or separate fund shall be established and no segregation of assets shall be made to assure payment.

12. Applicable Law. The validity, construction, interpretation and effect of this Agreement shall be governed by and construed in accordance with the laws of the State of Delaware, without giving effect to the conflicts of laws provisions thereof.

13. Notice. Any notice to POZEN provided for in this Agreement shall be addressed to POZEN in care of the Vice President, Finance and Administration, at the corporate headquarters of POZEN, and any notice to the Grantee shall be addressed to such Grantee at the current address shown on the payroll of POZEN, or to such other address as the Grantee may designate to POZEN in writing. Any notice shall be delivered by hand, sent by telecopy or enclosed in a properly sealed envelope addressed as stated above, registered and deposited, postage prepaid, in a post office regularly maintained by the United States Postal Service.

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IN WITNESS WHEREOF, POZEN has caused its duly authorized officer to execute this Restricted Stock Unit Agreement, and the Grantee has placed his signature hereon, effective as of the Date of Grant.

I hereby accept the award of Restricted Units described in this Agreement, and I agree to be bound by the terms of the Plan and this Agreement. I hereby agree that all of the decisions and determinations of the Committee with respect to the Restricted Units shall be final and binding.

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