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                                                                Exhibit 10.10(b)

                            MILLENNIUM CHEMICALS INC.

                                  Amendment To

                     MILLENNIUM PETROCHEMICALS GRANDFATHERED
                     SUPPLEMENTAL EXECUTIVE RETIREMENT PLAN

                                  (the "Plan")

     The Plan shall be, and it hereby is, amended effective June 1, 2002 as
     follows:

1.   Section 11.3 Change in Control

     Amend section to read in its entirety as follows:

     11.3 Change in Control

     The Plan will terminate effective on the close of business 30 days
     following a Change in Control, as hereinafter defined. Upon such Change in
     Control, section 12.1 shall become inoperative and, in addition, any
     modification or amendment adopted within six months prior to the Change in
     Control shall be void with respect to any specific Participant affected
     thereby unless approved by such Participant. Upon such termination, each
     Participant (including each Participant whose employment was terminated
     within six months prior to such Change in Control by the Employer without
     Cause, or due to disability, or voluntarily for good reason as determined
     by the Committee and each Participant that has experienced a Change of
     Control pursuant to a separate written "Change in Control" agreement with
     the Company or the Employer) will be deemed retired pursuant to Section 5.1
     based on Benefit Service through the termination date. A lump sum amount
     that is the actuarial equivalent of each Participant's benefit payable
     under this Plan shall be calculated using the prime rate of interest at
     Citigroup, Inc. as of the date of the Change in Control or 6%, whichever is
     less, as the discount rate to determine the present value of accrued
     benefits, shall be paid as soon as practicable following the date of the
     Change in Control, but in no event later than 90 days thereafter. All other
     actuarial assumptions and calculation methods to be used shall be those in
     effect as at the last actuarial valuation of the Qualified Plan and based
     on the Qualified Plan document prior to such Change in Control.

     For the purposes of this Plan, the term "Change in Control" shall mean (i)
     any "person" as such term is used in Sections 13(d) and 14(d) of the
     Securities Exchange Act of 1934 ("Act") (other than the Company, any
     trustee or other fiduciary holding securities under any employee benefit
     plan of the Company or any company owned, directly or indirectly, by the
     stockholders of the Company in substantially the same proportions as their
     ownership of Common Stock of the




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     Company), becoming the "beneficial owner" (as defined in Rule 13d-3 under
     the Act), directly or indirectly, of securities of the Company representing
     twenty-five percent (25%) or more of the combined voting power of the
     Company's then outstanding securities; (ii) during any period of two
     consecutive years (not including any period prior to October 1, 1996),
     individuals who at the beginning of such period constitute the Board of
     Directors of the Company, and any new director (other than a director
     designated by a person who has entered into an agreement with the Company
     to effect a transaction described in clause (i), (iii), or (iv) of this
     paragraph or a director 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 of Regulation 14A promulgated under the Act) or
     other actual or threatened solicitation of proxies or consents by or on
     behalf of a person other than the Board of Directors of the Company) whose
     election by the Board of Directors or nomination for election by the
     Company's stockholders was approved by a vote of at least two-thirds of the
     directors then still in office who either were directors at the beginning
     of the two-year period or whose election or nomination for election was
     previously so approved, cease for any reason to constitute at least a
     majority of the Board of Directors; (iii) the merger or consolidation of
     the Company with any other corporation, other than a merger or
     consolidation which would result in the voting securities of the Company
     outstanding immediately prior thereto continuing to represent (either by
     remaining outstanding or by being converted into voting securities of the
     surviving entity) more than fifty percent (50%) of the combined voting
     power of the voting securities of the Company or such surviving entity
     outstanding immediately after such merger or consolidation; provided,
     however, that a merger or consolidation effected to implement a
     recapitalization of the Company (or similar transaction) in which no person
     (other than those covered by the exceptions in (i) above) acquires more
     than twenty-five percent (25%) of the combined voting power of the
     Company's then outstanding securities shall not constitute a Change in
     Control or (iv) the stockholders of the Company approve a plan of complete
     liquidation of the Company or the closing of the sale or disposition by the
     Company of all or substantially all of the Company's assets other than the
     sale or disposition of all or substantially all of the assets of the
     Company to one or more Subsidiaries (as defined below) of the Company or to
     a person or persons who beneficially own, directly or indirectly, at least
     fifty percent (50%) or more of the combined voting power of the outstanding
     voting securities of the Company at the time of the sale or disposition;
     provided, however, (y) the sale or disposition of all or any part of the
     Company's interests in Equistar (and all subsequent sales and dispositions
     of any securities or assets received as proceeds thereof, or as proceeds of
     proceeds) shall not be deemed to constitute a Change in Control, and (z) if
     the Company's sells or disposes of all or any part of the Company's
     interests in Equistar indirectly (either through the sale or other
     disposition of any entity that owns, directly or indirectly, all or any
     part of the Company's interests in Equistar, or otherwise), then the sale
     or disposition of the Company's interests in Equistar (and all subsequent
     sales and dispositions of any securities or assets received as proceeds
     thereof, or as proceeds of proceeds) shall be ignored and disregarded in
     determining whether any such




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     Change in Control has occurred. By way of illustration, if an indirect
     subsidiary of the Company that owns the Company's interests in Equistar
     together with certain other assets is sold, then, in determining whether a
     Change in Control has occurred, all relevant determinations shall be made
     pursuant to the assumption that (y) such subsidiary owns only such other
     assets, and (z) neither such subsidiary nor the Company owns, either
     directly or indirectly, the interests in Equistar. "Subsidiary" shall have
     the meaning set forth in Section 424 of the Code and the term shall also
     include any partnership, limited liability company or other business entity
     if the Company owns directly or indirectly, securities or other ownership
     interests representing at least fifty percent (50%) of the ordinary voting
     power or equity or capital interests of such entity. Only one (1) Change in
     Control may take place under this Plan."