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                                                                  Exhibit 4.6(b)

                   AGREEMENT OF SUBSTITUTION AND AMENDMENT OF
                                RIGHTS AGREEMENT

         This Agreement of Substitution and Amendment is entered into as of
January 1, 2003, by and between Lyondell Chemical Company, a Delaware
corporation (the "Company") and American Stock Transfer and Trust Company, a New
York banking corporation ("AST").

                                    RECITALS

A.       On or about December 8, 1995, the Company entered into a Rights
         Agreement with The Bank of New York (the "Predecessor Agent") as rights
         agent, which was amended as of August 22, 2002 (as amended, the "Rights
         Agreement").

B.       The Company wishes to remove the Predecessor Agent and substitute AST
         as rights agent pursuant to Section 21 of the Rights Agreement.

C.       The Company has given the Predecessor Agent notice of removal of the
         Predecessor Agent as rights agent.

                                   AGREEMENT

         NOW THEREFORE, in consideration of the foregoing and of other
consideration, the sufficiency of which is hereby acknowledged, the parties
agree as follows:

1.       Section 21 of the Rights Agreement is hereby amended to provide that
         any successor rights agent shall, at the time of its appointment as
         rights agent, have a combined capital and surplus of at least $10
         million, rather than $50 million.

2.       The Company hereby appoints AST as rights agent pursuant to Section 21
         of the Rights Agreement, to serve in that capacity for the
         consideration and subject to all of the terms and conditions of the
         Rights Agreement.

3.       AST hereby accepts the appointment as rights agent pursuant to Section
         21 of the Rights Agreement and agrees to serve in that capacity for the
         consideration and subject to all of the terms and conditions of the
         Rights Agreement.

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4.       From and after the effective date hereof, each and every reference in
         the Rights Agreement to a "Rights Agent" shall be deemed to be a
         reference to AST.

5.       Section 26 of the Rights Agreement is amended to provide that notices
         or demands shall be addressed as follows (until another address is
         filed):

         If to the Company: Lyondell Chemical Company
                            ATTN: Kerry A. Galvin, General Counsel
                            1221 McKinney, Suite 700
                            Houston, TX 77010

         If to AST:         American Stock Transfer & Trust Company
                            59 Maiden Lane
                            New York, NY 10038
                            Attention: Corporate Trust Department

6.       Except as expressly modified herein, the Right Agreement shall remain
         in full force and effect.

7.       This Agreement of Substitution and Amendment may be executed in one or
         more counterparts, each of which shall together constitute one and the
         same document.

         IN WITNESS WHEREOF, the parties have caused this Agreement to be duly
executed as of the dated indicated above.

                                    LYONDELL CHEMICAL COMPANY


                              By:       /s/Kerry A. Galvin
                                    --------------------------------------------
                                    Kerry A. Galvin
                                    Senior Vice President, General Counsel and
                                    Secretary


                                    AMERICAN STOCK TRANSFER &
                                    TRUST COMPANY

                              By:       /s/ Herbert J. Lemmer
                                    --------------------------------------------
                                    Name: Herbert J. Lemmer
                                    Title: Vice President