Exhibit 10.1(b)

INSTRUMENT AMENDING

LYONDELL CHEMICAL COMPANY

EXECUTIVE SUPPLEMENTARY SAVINGS PLAN

Lyondell Chemical Company hereby amends the Lyondell Chemical Company Executive
Supplementary Savings Plan (“Plan”) by the addition of a new Termination Section
at the end thereof which shall provide as follows:

Section 14. Termination

14.1 Applicability of this Termination Section: The provisions of this
Termination Section 14 shall (i) override and supersede any conflicting terms
and provisions of the Plan and (ii) shall be effective as of January 1, 2009
(the “Termination Date”).

14.2 Eligibility: Notwithstanding any contrary provision of this Plan, no
Employee shall participate in the Plan on or after the Termination Date.

14.3 Cessation of Contributions: Notwithstanding any contrary provision of this
Plan, no contributions shall be made to the Plan for periods on or after the
Termination Date.

IN WITNESS WHEREOF, the undersigned, being duly authorized on behalf of the
Company, has executed this Instrument on this 15th day of December, 2008.

 

ATTEST:   LYONDELL CHEMICAL COMPANY BY:  

/s/ Mindy G. Davidson

  BY:  

/s/ Gerald A. O’Brien

  Assistant Secretary     Gerald A. O’Brien       Vice President and General
Counsel