Form of Restricted Stock Agreement (Non-Employee Director)

EXHIBIT 10.4

REMINGTON OIL AND GAS CORPORATION

2004 STOCK INCENTIVE PLAN

RESTRICTED STOCK AGREEMENT

(Non-employee Directors)

      1. Agreement to Grant Restricted Shares. Subject to the conditions described in this agreement (the “Agreement”) and the Remington Oil and Gas 2004 Stock Incentive Plan (the “Plan”), Remington Oil and Gas Corporation, a Delaware corporation (the “Company”), hereby agrees to grant to                                          (“Participant”) all rights, title and interest in the record and beneficial ownership of                      (     ) shares (the “Restricted Shares”) of common stock, $0.01 par value per share, of the Company (“Common Stock”). The grant of such Restricted Shares shall be effective as of                      (the “Grant Date”). All capitalized terms not otherwise defined herein shall have the meanings set forth in the Plan, the terms of which are incorporated herein by reference.

      2. Issuance and Transferability. Certificates representing the shares granted hereunder shall be issued to Participant pursuant to the terms of the Plan as of the Grant Date and shall be marked with the following legend:

“The shares represented by this certificate have been issued pursuant to the terms of the Remington Oil and Gas Corporation 2004 Stock Incentive Plan and may not be sold, pledged, transferred, assigned or otherwise encumbered in any manner except as is set forth in the terms of such Plan or Award dated                     .”

Until all restrictions lapse, the Restricted Stock shall not be transferable except by will or the laws of descent and distribution or pursuant to a domestic relations order of the court in a divorce proceeding. No right or benefit hereunder shall in any manner be liable for or subject to any debts, contracts, liabilities, or torts of Participant. Notwithstanding the foregoing, in the case of Participant’s death or Disability, Participant’s rights under this Agreement may be exercised by Participant’s guardian or legal representative. Any purported assignment, alienation, pledge, attachment, sale, transfer or other encumbrance of the Restricted Stock, prior to the lapse of restrictions, that does not satisfy the requirements hereunder shall be void and unenforceable against the Company.

      3. Risk of Forfeiture. Participant shall immediately forfeit all rights pursuant to this Agreement and to any nonvested portion of the Restricted Shares in the event of Participant’s resignation or removal from the Board of Directors of the Company under circumstances that do not cause Participant to become fully vested under the terms of this Agreement.

      4. Vesting. Subject to Paragraph 3 hereof and the terms of the Plan, Participant shall vest in all rights under the Restricted Shares and any rights of the Company to such shares shall lapse with respect to the Restricted Shares on the earlier of (i) the dates set forth below; (ii) a Change in Control; (iii) Participant’s Disability; (iv) Participant’s death; (v) Participant attains age 75 and terminates service on the Board; or (vi) the “Performance Vesting Date” described below. If

not earlier vested, the Restricted Shares shall vest according to the following schedule, provided that the Participant continuously serves on the Board of Directors from the Grant Date to the applicable vesting date:

Notwithstanding the foregoing, all Restricted Shares shall become fully vested on the date that the closing price per share of the Company’s Common Stock equals or exceeds two (2) times the closing price per share of such stock on April 13, 2005 ($     ) on the New York Stock Exchange, or such other exchange or market on which such shares primarily trade (the “Performance Vesting Date”). Upon vesting of the Restricted Shares, the Committee shall issue and deliver to Participant a certificate for such shares without the legend set forth in Section 2 above for the number of shares that are no longer subject to such restrictions.

      5. Ownership Rights/Dividends. Subject to the reservations set forth in this Agreement, the Plan and Paragraph 8, upon Participant’s receipt of the Restricted Shares, Participant shall be entitled to all voting and ownership rights applicable to the Restricted Shares, including the right to receive any cash dividends that may be paid on the Restricted Shares. The Restricted Shares shall be registered in the name of the Participant and at the address set forth below the Participant’s signature attached hereto. In addition, in the event of payment of any dividends on shares of Common Stock after October 14, 2004 and prior to issuance of the Restricted Shares, Participant shall receive a cash payment equal to the dividends paid with respect to an equivalent number of shares of Common Stock. Such payment shall be made to Participant within thirty days of the issuance of the Restricted Shares.

      6. Reorganization of the Company. The existence of this Agreement shall not affect in any way the right or power of the Company or its stockholders to make or authorize any or all adjustments, recapitalizations, reorganizations or other changes in the Company’s capital structure or its business; any merger or consolidation of the Company; any issue of bonds, debentures, preferred or prior preference stock ahead of or affecting the Restricted Shares or the rights thereof; the dissolution or liquidation of the Company, or any sale or transfer of all or any part of its assets or business, or any other corporate act or proceeding, whether of a similar character or otherwise.

      7. Recapitalization Events. In the event of stock dividends, spin-offs of assets or other extraordinary dividends, stock splits, combinations of shares, recapitalizations, mergers, consolidations, reorganizations, liquidations, issuances of rights or warrants and similar transactions or events involving the Company (“Recapitalization Events”), then for all purposes references herein to Common Stock or to Restricted Shares shall mean and include all securities or other property (other than cash) that holders of Common Stock of the Company are entitled to receive in respect of Common Stock by reason of each successive Recapitalization Event, which securities or other property (other than cash) shall be treated in the same manner and shall be subject to the same restrictions as the underlying Restricted Shares.

      8. Certain Restrictions. By executing this Agreement, Participant acknowledges that he will enter into such written representations, warranties and agreements and execute such

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documents as the Company may reasonably request in order to comply with the securities law or any other applicable laws, rules or regulations, or with this document or the terms of the Plan.

      9. Amendment. No amendment or termination of this Agreement shall be made by the Company at any time without the written consent of Participant.

      10. Withholding of Taxes. Participant agrees that, if he makes an election under Section 83(b) of the Internal Revenue Code of 1986, as amended, with regard to the Restricted Shares, he will so notify the Company in writing within two (2) days after making such election, so as to enable the Company to timely comply with any applicable governmental reporting requirements.

      11. No Guarantee of Tax Consequences. The Company makes no commitment or guarantee to Participant that any federal or state tax treatment will apply or be available to any person eligible for benefits under this Agreement.

      12. Severability. In the event that any provision of this Agreement shall be held illegal, invalid, or unenforceable for any reason, such provision shall be fully severable and shall not affect the remaining provisions of this Agreement, and the Agreement shall be construed and enforced as if the illegal, invalid, or unenforceable provision had never been included herein.

      13. Governing Law. This Agreement shall be construed in accordance with the laws of the State of Delaware to the extent federal law does not supersede and preempt Delaware law.

      Executed the       day of                      2005.

      Accepted the       day of                     , 2005

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