SECOND SUPPLEMENTAL INDENTURE dated as of August 16, 2006

Exhibit 4.13(b)

SECOND SUPPLEMENTAL INDENTURE

dated as of August 16, 2006

among

LYONDELL CHEMICAL COMPANY,

as Company

the SUBSIDIARY GUARANTORS party hereto

and

THE BANK OF NEW YORK,

as Trustee

11 ¹/8% Senior Secured Notes due 2012

THIS SECOND SUPPLEMENTAL INDENTURE (this “Supplemental Indenture”), entered into as of August 16, 2006, among LYONDELL CHEMICAL COMPANY, a Delaware corporation (the “Company”), LYONDELL-CITGO REFINING LP, a Delaware limited partnership, LYONDELL HOUSTON REFINERY INC., a Delaware corporation, and LYONDELL HOUSTON REFINERY A INC., a Delaware corporation (each an “Undersigned”), and THE BANK OF NEW YORK, as trustee (the “Trustee”).

RECITALS

WHEREAS, the Company, the Subsidiary Guarantors party thereto and the Trustee entered into the Indenture, dated as of July 2, 2002 (the “Indenture”), relating to the Company’s 11 ¹/8% Senior Secured Notes due 2012 (the “Notes”);

WHEREAS, as a condition to the Trustee entering into the Indenture and the purchase of the Notes by the Holders, the Company agreed, subject to certain exceptions, pursuant to Section 4.22 of the Indenture to cause any Restricted Subsidiary that has guaranteed or secured Indebtedness of the Company or any of its Restricted Subsidiaries to provide Subsidiary Guarantees.

AGREEMENT

NOW, THEREFORE, in consideration of the premises and mutual covenants herein contained and intending to be legally bound, the parties hereto hereby agree as follows:

Section 1. Capitalized terms used herein and not otherwise defined herein are used as defined in the Indenture.

Section 2. Each Undersigned, by its execution of this Supplemental Indenture, agrees to be a Subsidiary Guarantor under the Indenture and to be bound by the terms of the Indenture applicable to Subsidiary Guarantors, including, but not limited to, Article 13 thereof.

Section 3. This Supplemental Indenture shall be governed by and construed in accordance with the internal laws of the State of New York.

Section 4. This Supplemental Indenture may be signed in various counterparts which together shall constitute one and the same instrument.

Section 5. This Supplemental Indenture is an amendment supplemental to the Indenture and said Indenture and this Supplemental Indenture shall henceforth be read together.

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2

IN WITNESS WHEREOF, the parties have duly executed and delivered this Supplemental Indenture or have caused this Supplemental Indenture to be duly executed on their respective behalf by their respective officers thereunto duly authorized, as of the day and year first above written.

Signature Page to Supplemental Indenture

Signature Page to Supplemental Indenture