AMENDMENT NO. 1 to the Syntroleum Corporation Secured Promissory Note Dated May 8, 2002

Exhibit 10.6

AMENDMENT NO. 1

to the

Syntroleum Corporation Secured Promissory Note

Dated May 8, 2002

THIS AMENDMENT (the “Amendment”) is made and entered into on the 9th day of June 2004, being effective as of the 9th day of June 2004 (“Effective Date”), by and between MARATHON OIL COMPANY, an Ohio corporation (“Lender”), and SYNTROLEUM CORPORATION, a Delaware corporation (“Borrower”).

WHEREAS, Lender and Borrower are parties to a Syntroleum Corporation Secured Promissory Note (“Note”) entered into as of the 8th day of May 2002, pursuant to which Lender agreed to lend to Borrower up to $19.0 million upon the terms and conditions contained therein;

WHEREAS, the parties desire to amend certain terms and conditions of the Note as set forth herein.

NOW THEREFORE, in consideration of the mutual agreements contained herein and other good and valuable consideration, receipt of which is hereby acknowledged, the parties hereby agree as follows:

SECTION 1. Definitions. For purposes of this Amendment, terms used herein and not otherwise defined herein shall have the meanings as set forth in the Note.

SECTION 2. Amendment to Section 1(k). The definition of Maturity Date set forth in Section 1(k) is hereby deleted in its entirety and is hereby replaced with the following: “Maturity Date means June 30, 2005.”

SECTION 3. Amendment to Section 4(a). Section 4(a) of the Note is hereby deleted in its entirety and replaced with the following:

Borrower may prepay, from the Effective Date until and including the Maturity Date, in cash, in whole or in part and without penalty, the outstanding principal balance, together with accrued interest to date of payment, of this Note upon five (5) days written notice to Lender.

SECTION 4. Amendment to Section 4(c). Section 4(c) is hereby deleted in its entirety.

SECTION 5. Amendment to Section 4(d). The language contained in the leadin paragraph of this section, which states “or has not been converted pursuant to any of the provisions contained in this Section 4 prior to the Maturity Date”, is hereby deleted.

SECTION 6. Effective Date. This Amendment shall become effective on the Effective Date.

SECTION 7. Instrument Pursuant to Note. This Amendment is executed pursuant to the Note and shall (unless otherwise expressly indicated herein) be construed, administered and applied in accordance with all of the terms and provisions thereof. Except as expressly amended hereby, all of the representations, warranties, terms, covenants, conditions and other provisions of the Note shall remain unamended and shall continue in full force and effect in accordance with the provisions thereof as in existence on the date hereof. The amendment set forth herein shall be limited precisely as provided for herein and shall not be deemed to be a waiver of, amendment of, consent to or modification of any other term or provision of the Note, or except as contemplated herein, of any term or provision of any other document contemplated thereby. After the Effective Date, any reference to the Note shall mean the Note as amended hereby.

SECTION 8. Successors and Assigns. This Amendment shall be binding upon and inure to the benefit of the parties hereto and their respective permitted successors and assigns.

SECTION 9. Counterparts. This Amendment may be executed by the parties hereto in any number of counterparts, each of which when so executed shall be deemed to be an original and all of which when taken together shall constitute together one and the same agreement.

SECTION 10. Governing Law. This Amendment shall be construed and enforced in accordance with the laws of the State of Oklahoma, without regard to the conflict of law provisions thereof.

SECTION 11. Headings. The headings of this Amendment are for the purposes of reference only and shall not limit or otherwise affect the meaning hereof.

SECTION 12. Amendments. No waiver, amendment or other modification of any of the terms or provisions of this Amendment shall be effective without the written consent of each party hereto.

IN WITNESS WHEREOF, the parties hereto have executed this Amendment by their respective officers or agents thereunto authorized.