FOURTH SUPPLEMENTAL INDENTURE

Exhibit 4.17

FOURTH SUPPLEMENTAL INDENTURE

This Fourth Supplemental Indenture (this “Supplemental Indenture”), dated as of May 3, 2011, is entered into by and among Southwest Airlines Co., a Texas corporation (“Southwest” or the “Company”), AirTran Airways, Inc., a Delaware corporation (the “Guarantor”), and Wilmington Trust Company, a Delaware banking corporation, as trustee hereunder (the “Trustee”). Capitalized terms used herein and not otherwise defined have the meanings set forth in the Indenture (as defined below).

WHEREAS, AirTran Holdings, Inc., a Nevada corporation (“AirTran Holdings Inc”), the Guarantor, and the Trustee are parties to an Indenture dated as of May 7, 2003 relating to the issuance of the 7% Convertible Notes due 2023 (the “Base Indenture”);

WHEREAS, AirTran Holdings Inc, the Guarantor, Southwest and the Trustee entered into a First Supplemental Indenture dated as of May 2, 2011, which supplements the Base Indenture (the “First Supplemental Indenture”);

WHEREAS, the Guarantor, Southwest, AirTran Holdings, LLC, a Texas limited liability company (“AirTran LLC”), and the Trustee entered into a Second Supplemental Indenture dated as of May 2, 2011, which supplements the Base Indenture and the First Supplemental Indenture (the “Second Supplemental Indenture”);

WHEREAS, the Guarantor, Southwest, Pedernales Debt Sub, LLC, a Texas limited liability company (“TX Debt Sub”), and the Trustee entered into a Third Supplemental Indenture dated as of May 3, 2011, which supplements the Base Indenture, the First Supplemental Indenture and the Second Supplemental Indenture (the “Third Supplemental Indenture” and, the Base Indenture as supplemented by the First Supplemental Indenture, the Second Supplemental Indenture and the Third Supplemental Indenture, the “Indenture”);

WHEREAS, Southwest and TX Debt Sub entered into the Agreement and Plan of Merger dated as of May 3, 2011, pursuant to which, at the effective time of the merger contemplated thereby, TX Debt Sub was merged with and into Southwest such that the separate corporate existence of TX Debt Sub ceased and Southwest continued as the surviving corporation (the “Merger”)

WHEREAS, pursuant to Section 11.01 of the Indenture, subject to the provisions of Section 11.02 of the Indenture, nothing contained in the Indenture or in any of the Notes shall prevent the Merger; provided that upon the Merger, the due and punctual payment of the principal of and premium, if any, and interest on all of the Notes, according to their tenor and the due and punctual performance and observance of all of the covenants and conditions of the Indenture to be performed by TX Debt Sub, shall be expressly assumed, by a supplemental indenture satisfactory in form to the Trustee, executed and delivered to the Trustee by Southwest;

WHEREAS, in accordance with Section 10.01 of the Base Indenture, the Company, the Guarantor and the Trustee may amend or supplement the Indenture as provided in this Supplemental Indenture without the consent of the holders of the Notes; and

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WHEREAS, each of the Company and the Guarantor have duly authorized the execution and delivery of this Supplemental Indenture;

NOW, THEREFORE, the parties hereto covenant and agree for the equal and proportionate benefit of all Holders of the Notes, as follows:

ARTICLE I

ASSUMPTION

Section 1.01 Assumption. The due and punctual payment of the principal of and premium, if any, and interest on all of the Notes, according to their tenor and the due and punctual performance and observance of all of the covenants and conditions of the Indenture to be performed by TX Debt Sub, are hereby expressly assumed by the Company.

Section 1.02 Successor Substituted. In accordance with Section 11.02 of the Base Indenture, the Company hereby succeeds to and is substituted for TX Debt Sub, with the same effect as if the Company had been named in the Indenture as TX Debt Sub.

ARTICLE II

Definitions

Section 2.01 Definitions. Section 1.01 of the Base Indenture is hereby amended as follows:

(a) The definition of “Common Stock” and “Southwest” are hereby amended and restated in their entirety to read as one definition as follows:

“Company” and “Southwest” each mean Southwest Airlines Co., a Texas corporation, and, subject to the provisions of Article 11 and Section 14.06, shall include its successors and assigns. For all purposes of the Indenture, the Company means Southwest and Southwest means the Company, mutatis mutandis. Any reference to both Southwest and the Company shall hereafter mean only Southwest.

ARTICLE III

MISCELLANEOUS PROVISIONS

Section 3.01 Concerning the Trustee. The Trustee assumes no duties, responsibilities, or liabilities by reason of this Supplemental Indenture other than as set forth in the Indenture. The Trustee shall not be responsible in any manner whatsoever for or in respect of the validity or sufficiency of this Supplemental Indenture or for or in respect of the recitals contained herein, all of which recitals are made solely by the Guarantor and Southwest.

Section 3.02 Supplemental Indenture Controls. In the event of a conflict or inconsistency between the Indenture and this Supplemental Indenture, the provisions of this Supplemental Indenture shall control.

Section 3.03 Governing Law. This Supplemental Indenture shall be deemed to be a contract made under the laws of the State of New York, and for all purposes shall be construed in accordance with the laws of the State of New York, without regard to conflicts of laws principles thereof.

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Section 3.04 Execution in Counterparts. This Supplemental Indenture may be executed in any number of counterparts, each of which shall be an original, but such counterparts shall together constitute but one and the same instrument.

Section 3.05 Confirmation of Indenture. Except as supplemented hereby, the Indenture is hereby ratified, confirmed, and reaffirmed in all respects. The Indenture and this Supplemental Indenture shall be read, taken, and construed as one and the same instrument.

Section 3.06 Headings. The titles and headings of the articles and sections of this Supplemental Indenture have been inserted for convenience of reference only, are not to be considered a part hereof, and shall in no way modify or restrict any of the terms or provisions hereof.

[Signature Pages Follow]

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IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture to be duly executed.

Signature Page to Fourth Supplemental Indenture

IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture to be duly executed.

Signature Page to Fourth Supplemental Indenture

IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture to be duly executed.

Signature Page to Fourth Supplemental Indenture