INSTRUMENT AMENDING

Exhibit 10.12(b)

INSTRUMENT AMENDING

LYONDELL CHEMICAL COMPANY

RETIREMENT PLAN FOR NON-EMPLOYEE DIRECTORS

Lyondell Chemical Company hereby amends the Retirement Plan for Non-Employee Directors, effective as of March 28, 2004, as follows:

ARTICLE V, CHANGE IN CONTROL, Section 5.3, is revised in its entirety to read as follows:

5.3 For purposes of this Plan, a Change in Control will be deemed to have occurred as of the date that one or more of the following occurs:

(a) Individuals who, on the date of this amendment, constitute the entire Board (“Incumbent Directors”) 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 Company’s shareholders, was approved by a vote of at least a majority of the then Incumbent Directors shall be considered as though such individual was an Incumbent Director, but excluding, for this purpose any such individual whose initial assumption of office occurs as a result of either an actual or threatened election contest, as such terms are used in Rule 14a-11 under the Securities Exchange Act of 1934, as amended or other actual or threatened solicitation of proxies or consents by or on behalf of any Person (as defined below) other than the Board;

(b) The stockholders of the Company shall approve any merger, consolidation or recapitalization of the Company (or, if the capital stock of the Company is affected, any subsidiary of the Company), or any sale, lease, or other transfer (in one transaction or a series of transactions contemplated or arranged by any party as a single plan) of all or substantially all of the assets of the Company (each of the foregoing being an “Acquisition Transaction”) where (1) the shareholders of the Company immediately prior to such Acquisition Transaction would not immediately after such Acquisition Transaction beneficially own, directly or indirectly, shares or other ownership interests representing in the aggregate eighty percent (80%) or more of (A) the then outstanding common stock or other equity interests of the corporation or other entity surviving or resulting from such merger, consolidation or recapitalization or acquiring such assets of the Company, as the case may be, or of its ultimate parent corporation or other entity, if

any (in either case, the “Surviving Entity”), and (B) the Combined Voting Power of the then outstanding Voting Securities of the Surviving Entity or (2) the Incumbent Directors at the time of the initial approval of such Acquisition Transaction would not immediately after such Acquisition Transaction constitute a majority of the Board of Directors, or similar managing group, of the Surviving Entity; provided, however, that, notwithstanding the foregoing, a Change of Control shall not be deemed to have occurred for purposes of this Subsection (b) if each of the following conditions are met: (i) the Acquisition Transaction is between the Company and/or its Affiliates, on the one hand, and Millennium Chemicals Inc. (“Millennium”) and/or its Affiliates, on the other hand, (ii) the Company or an entity that was a wholly owned subsidiary of the Company prior to the Acquisition Transaction has a class of equity securities registered under Section 12 of the Securities Exchange Act of 1934, as amended, immediately after completion of the Acquisition Transaction, and (iii) as a result of the Acquisition Transaction, the Company or its Affiliates own a greater percentage equity interest in Equistar Chemicals, LP (“Equistar”) than was owned, directly or indirectly, by the Company immediately prior to such Acquisition Transaction;

(c) The stockholders of the Company shall approve any plan or proposal for the liquidation or dissolution of the Company; or

(d) Any Person shall be or become the beneficial owner (as defined in Rules 13d-3 and 13d-5 under the Securities Exchange Act of 1934, as amended), directly or indirectly, of securities of the Company representing in the aggregate more than twenty percent (20%) of either (A) the then outstanding shares of common stock of the Company (“Common Shares”) or (B) the Combined Voting Power of all then outstanding Voting Securities of the Company; provided, however, that notwithstanding the foregoing, a Change in Control shall not be deemed to have occurred for purposes of this Subsection (d):

(1) Solely as a result of an acquisition of securities by the Company which, by reducing the number of Common Shares or other Voting Securities outstanding, increases (a) the proportionate number of Common Shares beneficially owned by any Person to more than twenty percent (20%) of the Common Shares then outstanding, or (b) the proportionate voting power represented by the Voting Securities beneficially owned by any Person to more than twenty percent (20%) of the Combined Voting Power of all then outstanding Voting Securities;

(2) Solely as a result of an acquisition of securities directly from the Company, except for any conversion of a security that was not acquired directly from the Company; or

(3) Solely as a result of a direct or indirect acquisition by Occidental Petroleum Corporation (“Occidental”) or Millennium, or any Affiliate of either of them, of beneficial ownership of securities representing, (x) in the case of Occidental (with its Affiliates), no more than forty percent (40%), (y) in the case of Millennium (with its Affiliates), no more than forty percent (40%), and (z) in the case of Occidental (with its Affiliates) and Millennium (with its Affiliates) in

the aggregate, no more than forty-nine percent (49%), of either (A) the then outstanding Common Shares or (B) the Combined Voting Power of all then outstanding Voting Securities of the Company, pursuant to or as contemplated under any agreement between the Company and Occidental and/or Millennium or Affiliates of either of them (including any subsequent related transaction or series of related transactions or acquisitions of Voting Securities of the Company by Occidental and/or Millennium or their Affiliates or assignees approved by the Incumbent Directors prior to the consummation of such transaction or series of related transactions) where, as a result of such transaction or series of related transactions, the Company or a Surviving Entity owns, directly or indirectly, a greater percentage equity interest in Equistar than was owned, directly or indirectly, by the Company immediately prior to such transaction or series of related transactions;

provided, further, that if any Person referred to in paragraph (1) or (2) of this Subsection (d) shall thereafter become the beneficial owner of additional shares or other ownership interests representing one percent (1%) or more of the outstanding Common Shares or one percent (1%) or more of the Combined Voting Power of the Company (other than (x) pursuant to a stock split, stock dividend or similar transaction or (y) as a result of an event described in paragraph (1), (2) or (3) of this Subsection (d)), then a Change in Control shall be deemed to have occurred for purposes of this Subsection (d).

(e) For purposes of this definition of Change in Control, the following capitalized terms have the following meanings:

(1) “Affiliate” shall mean, as to a specified person, another person that directly, or indirectly through one or more intermediaries, controls or is controlled by, or is under common control with, the specified person, within the meaning of such terms as used in Rule 405 under the Securities Act of 1933, as amended, or any successor rule.

(2) “Combined Voting Power” shall mean the aggregate votes entitled to be cast generally in the election of the Board of Directors, or similar managing group, of a corporation or other entity by holders of then outstanding Voting Securities of such corporation or other entity.

(3) “Person” shall mean any individual, entity (including, without limitation, any corporation, partnership, trust, joint venture, association or governmental body) or group (as defined in Sections 14(d)(3) or 15(d)(2) of the Exchange Act and the rules and regulations thereunder); provided, however, that Person shall not include the Company, LYONDELL-CITGO Refining LP (“LCR”) or Equistar, any of their subsidiaries, any employee benefit plan of the Company, LCR or Equistar or any of their majority-owned subsidiaries or any entity organized, appointed or established by the Company, LCR, Equistar or such subsidiaries for or pursuant to the terms of any such plan.

(4) “Voting Securities” shall mean all securities of a corporation or other entity having the right under ordinary circumstances to vote in an election of

the Board of Directors, or similar managing group, of such corporation or other entity.

IN WITNESS WHEREOF, the undersigned, being duly authorized on behalf of the Company, has executed this Instrument on this 28th day of March, 2004.