UNOCAL CORPORATION

Exhibit 10.4(E)(4)

UNOCAL CORPORATION

Long-Term Incentive Plan of 1998

Performance Share Award

AGREEMENT

AGREEMENT effective as of January 1, 2003, between UNOCAL CORPORATION (hereinafter called the “Company”) and Name (hereinafter called the “Participant”).

1. Award Grant. The Company hereby awards to Participant Shares Performance Share Units (each unit shall be deemed to be the equivalent of one share of Common Stock of the Company). Such Performance Share Units will be credited to the Performance Share account maintained for Participant under the Long-Term Incentive Plan of 1998.

2. Rights to Payment of Performance Share Units. It is understood that the amount of the foregoing award earned and paid will be established by the Management Development and Compensation Committee of the Board of Directors of the Company (the “Committee”) based on how the Company’s Return to Stockholders compares to that of a group of companies (the “Peer Group Companies”) during the four-year Award Period which ends on December 31, 2006. “Return to Stockholders” is the sum of cash dividends and share price appreciation expressed as a percentage of the beginning share price. The actual payment of the Performance Share Units awarded will be determined in accordance with the following:

In the case of a percentile ranking falling between those indicated, payout percentage shall be determined using straight-line interpolation.

Under the foregoing formula, Participant will be entitled to payment of 100% of the Performance Share Units awarded if the Company’s Return to Stockholders is at the 60th percentile of the Return to Stockholders of the Peer Group Companies. However, in no event shall the Participant receive in excess of 200% of the Units awarded, and payment is further subject to the limitation contained in Section 3 below. Notwithstanding anything to the contrary stated above, the Committee may reduce the payment based on other factors at the discretion of the Committee.

The Committee has determined the Peer Group Companies to be used for purposes of the comparison of Return to Stockholders. During the Award Period no changes will be made by the Committee to the Peer Group Companies, except as required because of merger, dissolution or similar circumstance with respect to such companies.

3. Payment of Awards. Payments made hereunder shall be equal in amount to the Fair Market Value on the Valuation Date of the number of shares of Common Stock equivalent to the number of Performance Share Units earned and payable to Participant pursuant to paragraph 2 above, subject to a maximum Fair Market Value of not more than 400% of the Fair Market Value of such Performance Share Units at the time of granting the Performance Share Units. Payments shall be made on December 31, 2006 or as soon as practicable thereafter. The Committee will determine the form of payout, which will normally be partially in cash and partially in shares of the Company’s Common Stock.

Upon the occurrence of a Change in Control Event (as such term is defined below), each Performance Share Unit will become payable to the Participant (such Performance Share Award to be paid by the Company), solely in cash, as if the Award Period ended as of the occurrence of such Change in Control Event. The Committee may estimate average shareholder returns or other performance measures for any such period for which reports are not yet available. However, upon a Change of Control, participant shall receive not less than the number of Performance Share Units awarded, subject to limits indicated in the above paragraph. As used herein, “Change in Control Event” means any of the following:

(a) The acquisition by any individual, entity or group (within the meaning of Section 13(d)(3) or 14(d)(2) of the Securities Exchange Act of 1934, as amended (the “Exchange Act”)(a “Person”) of beneficial ownership (within the meaning of Rule 13d-3 promulgated under the Exchange Act) of 20% or more of either (i) the then outstanding shares of common stock of the Company (the “Outstanding Company Common Stock”) or (ii) the combined voting power of the then outstanding voting securities of the Company entitled to vote generally in the election of directors (the “outstanding Company Voting Securities”); provided, however, that for purposes of this subsection (a), the following acquisitions shall not constitute a Change of Control: (i) any acquisition directly from the Company, (ii) any acquisition by the Company, (iii) any acquisition by an employee benefit plan (or related trust) sponsored or maintained by the Company or any corporation controlled by the Company or (iv) any acquisition by any corporation pursuant to a transaction which complies with clauses (i), (ii) and (iii) of subsection (c) of this Section 3; or

(b) Individuals who, as of the date hereof, constitute the Board (the “Incumbent Board”) cease for any reason to constitute at least a majority of the Board; provided however, that any individual becoming a director subsequent to the date hereof whose election, or nomination for election by the

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Company’s shareholders, was approved by a vote of at least a majority of the directors then comprising the Incumbent Board shall be considered as though such individual were a member of the Incumbent Board, but excluding, for this purpose, any such individual whose initial assumption of office occurs as a result of an actual or threatened election contest with respect to the election or removal of directors or other actual or threatened solicitation of proxies or consents by or on behalf of a Person other than the Board; or

(c) The approval by the shareholders of the Company of a reorganization, merger or consolidation or sale or other disposition of all or substantially all of the assets of the Company or the acquisition of assets of another corporation (a “Business Combination”), or, if consummation of such Business Combination is subject, at the time of such approval by shareholders, to the consent of any government or governmental agency, the obtaining of such consent either explicitly or implicitly by consummation of the Business Combination in each case, unless, following such Business Combination, (i) all or substantially all of the individuals and entities who were the beneficial owners, respectively, of the Outstanding Company Common Stock and Outstanding Company Voting Securities immediately prior to such Business Combination will beneficially own, directly or indirectly, more than 50% of, respectively, the then outstanding shares of common stock and the combined voting power of the then outstanding voting securities entitled to vote generally in the election of directors, as the case may be, of the corporation resulting from such Business Combination (including, without limitation, a corporation which as a result of such transaction owns the Company or all or substantially all of the Company’s assets either directly or through one or more subsidiaries) in substantially the same proportions as their ownership, immediately prior to such Business Combination of the Outstanding Company Common Stock and Outstanding Company voting Securities, as the case may be, (ii) no Person (excluding any corporation resulting from such Business Combination or any employee benefit plan (or related trust) of the Company or such corporation resulting from such Business Combination) will beneficially own, directly or indirectly, 20% or more of, respectively, the then outstanding shares of common stock of the corporation resulting from such Business Combination or the combined voting power of the then outstanding voting securities of such corporation except to the extent that such ownership existed prior to the Business Combination and (iii) at least a majority of the members of the board of directors of the corporation resulting from such Business Combination will have been members of the Incumbent Board at the time of the execution of the initial agreement, or of the action of the Board, providing for such Business Combination; or

(d) Approval by the shareholders of the Company of a complete liquidation or dissolution of the Company.

Notwithstanding the foregoing, the Committee may, in its sole discretion, accelerate payments prior to the end of any Award Period in accordance with the provisions of the Plan.

If any right to acquire Stock and/or cash hereunder has been fully accelerated as required by this Section 3 and thus is or becomes payable solely in cash, the right shall be paid by the Company immediately prior to any dissolution of the Company, or any merger, reorganization, consolidation or similar event that the Company does not survive.

4. Termination of Employment. In the event Participant’s employment terminates during the Award Period, payouts will be as follows:

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5. Adjustment Provisions. In the event of any change in the outstanding shares of Common Stock by reason of any stock dividend or split, recapitalization, reclassification, merger, consolidation, combination or exchange of shares or similar corporate change, then the number or kind of Performance Share Units then held in Participants’ Performance Share accounts and the number of Performance Share Units which may be awarded under the Plan shall be adjusted proportionately. No adjustment will be made in connection with the payment by the Company of any cash dividend on its Common Stock or in connection with the issuance by the Company of any warrants, rights or options to acquire additional shares of Common Stock or of securities convertible into Common Stock.

6. No Rights of Stock Ownership. This award of Performance Share Units will not entitle Participant to any interest in or to any dividend, voting, or other rights normally attributable to Common Stock ownership.

7. Tax Withholding. The Company or a subsidiary, as appropriate, shall have the right to deduct from all awards any Federal, state, or local taxes required by law to be withheld with respect to such payments. In the case of awards paid in Common Stock, Participant may be required to pay to the Company or subsidiary, as appropriate, the amount of any such taxes which the Company or subsidiary is required to withhold with respect to such Stock prior to delivery of such Stock by Company unless the Company withholds stock to satisfy such withholding obligations.

8. Nonassignability. This award may not be assigned, pledged, or transferred except, in the event of death, to a designated beneficiary or by will or by the laws of descent and distribution. The foregoing restrictions shall not apply to transfers pursuant to a court order, including, but not limited to, any domestic relations order.

9. Effect Upon Employment. This Agreement is not to be construed as giving any right to Participant for continuous employment by the Company or a subsidiary. The Company and its subsidiaries retains the right to terminate an employee at will and with or without cause at any time.

10. Successors. This Agreement shall be binding upon any successor of the Company.

11. Terms. All terms used herein are used as defined in the Long-Term Incentive Plan of 1998 of the Company as amended and the summary of the terms of said Plan herein is qualified in its entirety by reference to the Plan itself. The Company and Committee retain all authority and powers granted by the Plan not expressly limited by this Agreement.

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IN WITNESS WHEREOF, the parties have signed this Agreement effective as of the date and year indicated above.

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BENEFICIARY DESIGNATION

UNOCAL CORPORATION

LONG-TERM INCENTIVE PLAN OF 1998

PERFORMANCE SHARE AWARD

I designate the following beneficiary or beneficiaries to receive any payment, in the event of my death, of any Performance Share Award heretofore or hereafter granted to me pursuant to the Long-Term Incentive Plan of 1998:

I may change the beneficiary or beneficiaries from time to time by filing with the Company a new Beneficiary Designation form.

I agree that the last designation received by the Company prior to my death shall control over any testamentary or other disposition I may make; however, if my spouse is one of the beneficiaries named above but is not my spouse at the time of my death, such designation shall be deemed revoked. I further agree that the Company may make payment to the legal representative of my estate if there is any question as to the right of any beneficiary to take hereunder, and the Company, its directors, the Compensation Committee and any member thereof, and any employee of the Company, shall have no further liability with respect thereto.