AMENDMENT NO. 4 TO THE EL PASO CORPORATION SUPPLEMENTAL BENEFITS PLAN

EXHIBIT 10.E.4

AMENDMENT NO. 4 TO THE

EL PASO CORPORATION

SUPPLEMENTAL BENEFITS PLAN

WHEREAS, El Paso Corporation (the “Company”) maintains the El Paso Corporation Supplemental Benefits Plan (the “Plan”);

WHEREAS, Section 6.7 of the Plan permits the Board of Directors or the Compensation Committee of the Board of Directors from time to time to amend, suspend or terminate the Plan, in whole or in part;

WHEREAS, by Resolution of the Company’s Board of Directors dated December 2, 2005, the Board of Directors amended the Plan, effective as of December 31, 2004, to cease all accruals thereunder other than interest credits or other earnings accrued following December 31, 2004 in respect of amounts accrued thereunder on or prior to December 31, 2004;

WHEREAS, it is intended hereby to amend the Plan in accordance with such Resolution;

NOW, THEREFORE, in accordance with the Resolution of the Board of Directors dated December 2, 2005, the Plan is amended as follows:

“6.10 Cessation of Accruals under the Plan

Notwithstanding any other provision of this Plan, effective as of December 31, 2004, the accrual of benefits under this Plan shall cease, other than interest credits and other earnings accrued following December 31, 2004 in respect of amounts accrued under the Plan on or prior to December 31, 2004. The intent of this Section 6.10 is to cause the Plan not to be subject to Section 409A of the Code.”

IN WITNESS WHEREOF, this amendment has been executed by the undersigned, thereunto duly authorized, effective as of December 2, 2005.