GUARANTEE

Exhibit 4.13

GUARANTEE

dated as of November 24, 2009

from

UAL CORPORATION

Twelve (12) Airbus A319-131 Aircraft

Five (5) Airbus A320-232 Aircraft

Seven (7) Boeing 757-222 Aircraft

Ten (10) Boeing 777-222 Aircraft and

Three (3) Boeing 747-422 Aircraft

TABLE OF CONTENTS

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GUARANTEE

THIS GUARANTEE, dated as of November 24, 2009 (as amended, modified or supplemented from time to time, this “Guarantee”), from UAL CORPORATION, a Delaware corporation (together with its permitted successors and assigns, the “Guarantor”), to the parties listed in Schedule I hereto (collectively, together with their successors and permitted assigns, the “Parties”, and, individually, a “Party”).

WHEREAS, United Air Lines, Inc., a Delaware corporation (“Owner”), a direct wholly-owned subsidiary of the Guarantor, has entered into that certain Note Purchase Agreement dated as of November 24, 2009 (the “Note Purchase Agreement”) among Owner, Wilmington Trust Company, as pass through trustee under each of the Pass Through Trust Agreements (the “Pass Through Trustee”), Wilmington Trust Company, as Escrow Agent under each of the Escrow Agreements, Wilmington Trust Company, as Paying Agent under each of the Escrow Agreements and Wilmington Trust Company, as Subordination Agent (the “Subordination Agent”);

WHEREAS, capitalized used but not defined herein shall have the meanings set forth in the Note Purchase Agreement;

WHEREAS, in order to finance the aircraft identified on Schedule II hereto (the “Aircraft”), Owner will issue the Equipment Notes under the Indentures; and

WHEREAS, it is a condition to the purchase of the Equipment Notes by the Pass Through Trustee that the Guarantor execute and deliver this Guarantee.

NOW, THEREFORE, in order to induce the Pass Through Trustee to purchase the Equipment Notes and for other good and valuable consideration, receipt of which is hereby acknowledged, the parties hereto agree as follows:

Section 1. Guarantee.

(a) The Guarantor does hereby acknowledge that it is fully aware of the terms and conditions of the Indentures, the Participation Agreements, the Equipment Notes and the transactions and the other documents contemplated thereby, and does hereby irrevocably and fully and unconditionally guarantee, as primary obligor and not as surety merely, to the Parties, as their respective interests may appear, the payment by Owner of all payment obligations when due under the Indentures, the Participation Agreements and the Equipment Notes (such obligations of Owner guaranteed hereby being hereafter referred to, individually, as a “Guaranteed Obligation” and, collectively, as the “Guaranteed Obligations”) in accordance with the terms of the Financing Agreements. The Guarantor does hereby agree that in the event that Owner fails to pay any Guaranteed Obligation when due for any reason (including, without limitation, the liquidation, dissolution, receivership, insolvency, bankruptcy, assignment for the benefit of creditors, reorganization, arrangement, composition or readjustment of, or other similar proceedings affecting the status, existence, assets or obligations of Owner, or the disaffirmance with respect to Owner of any Indenture or any other Financing Agreement to which Owner is a party in any such proceeding) after the date on which such Guaranteed Obligation became due and payable and the applicable grace period has expired, the Guarantor shall pay or cause to be paid forthwith, upon the receipt of notice from the Loan Trustee (such

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notice to be sent to Owner (to the extent the Loan Trustee is not stayed or prevented from doing so by operation of law) and the Guarantor) stating that such Guaranteed Obligation was not paid when due after the applicable grace period has expired and stating the amount of such Guaranteed Obligation.

(b) The obligations of the Guarantor hereunder shall not be, to the fullest extent permitted by law, affected by: the genuineness, validity, regularity or enforceability (or lack thereof) of any of Owner’s obligations under any Indenture or any other Financing Agreement to which Owner is a party, any amendment, waiver or other modification of any Indenture or such other Financing Agreement (except that any such amendment or other modification shall be given effect in determining the obligations of the Guarantor hereunder), or by any substitution, release or exchange of collateral for or other guaranty of any of the Guaranteed Obligations (except to the extent that such substitution, release or exchange is not undertaken in accordance with the terms of the Financing Agreements) without the consent of the Guarantor, or by any priority or preference to which any other obligations of Owner may be entitled over Owner’s obligations under any Indenture and the other Financing Agreements to which Owner is a party, or by any other circumstance that might otherwise constitute a legal or equitable defense to or discharge of the obligations of a surety or guarantor including, without limitation, any defense arising out of any laws of the United States of America of any State thereof which would excuse, discharge, exempt, modify or delay the due or punctual payment and performance of the obligations of the Guarantor hereunder. Without limiting the generality of the foregoing, it is agreed that the occurrence of any one or more of the following shall not, to the fullest extent permitted by law, affect the liability of the Guarantor hereunder: (a) the extension of the time for or waiver of, at any time or from time to time, without notice to the Guarantor, Owner’s performance of or compliance with any of its obligations under the Financing Agreements (except that such extension or waiver shall be given effect in determining the obligations of the Guarantor hereunder), (b) any assignment, transfer, lease or other arrangement by which Owner transfers possession or loses control of the use of any Aircraft, (c) any defect in the title, condition, design, operation or fitness for use of, or damage to or loss or destruction of, any Aircraft, whether or not due to the fault of Owner, (d) any merger or consolidation of Owner or the Guarantor into or with any other Person, or any sale, transfer, lease or disposal of any of its assets, (e) any issuance of Additional Equipment Notes or (f) any change in the ownership of any shares of capital stock of Owner.

(c) This Guarantee is an absolute, present and continuing guaranty of payment and performance and not of collection and is in no way conditional or contingent upon any attempt to collect from Owner any unpaid amounts due. The Guarantor specifically agrees, to the fullest extent permitted by law, that it shall not be necessary or required, and that the Guarantor shall not be entitled to require, that any Party (i) file suit or proceed to obtain or assert a claim for personal judgment against Owner for the Guaranteed Obligations, or (ii) make any effort at collection of the Guaranteed Obligations from Owner, or (iii) foreclose against or seek to realize upon any security now or hereafter existing for the Guaranteed Obligations, including the Collateral (as defined in the Indentures), or (iv) file suit or proceed to obtain or assert a claim for personal judgment against any other Person liable for the Guaranteed Obligations, or make any effort at collection of the Guaranteed Obligations from any such other Person, or exercise or assert any other right or remedy to which any Party is or may be entitled in connection with the Guaranteed Obligations or any

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security or other guaranty therefor, or (v) assert or file any claim against the assets of Owner or any other guarantor or other Person liable for the Guaranteed Obligations, or any part thereof, before or as a condition of enforcing the liability of the Guarantor under this Guarantee or requiring payment of said Guaranteed Obligations by the Guarantor hereunder, or at any time thereafter.

Section 2. No Implied Third Party Beneficiaries. This Guarantee shall not be deemed to create any right in any Person except a Party and shall not be construed in any respect to be a contract in whole or in part for the benefit of any other Person.

Section 3. Waiver; No Set-off; Reinstatement; Subrogation. The Guarantor waives notice of the acceptance of this Guarantee and of the performance or nonperformance by Owner, demand for payment from Owner or any other Person, notice of nonpayment or failure to perform on the part of Owner, diligence, presentment, protest, dishonor and, to the fullest extent permitted by law, all other demands or notices whatsoever, other than the request for payment hereunder and notice provided for in Section 1 hereof. The obligations of the Guarantor shall be absolute and unconditional and shall remain in full force and effect until satisfaction of all Guaranteed Obligations and, without limiting the generality of the foregoing, to the extent not prohibited by applicable law, shall not be released, discharged or otherwise affected by the existence of any claims, set-off, defense or other rights that the Guarantor may have at any time and from time to time against any Party, whether in connection herewith or any unrelated transactions. This Guarantee shall continue to be effective or be reinstated, as the case may be, if at any time any payment of any Guaranteed Obligation is rescinded or must otherwise be returned by any Party upon the insolvency, bankruptcy, reorganization, arrangement, readjustment of debt, dissolution, liquidation or similar proceeding with respect to Owner or otherwise, all as though such payment had not been made. The Guarantor, by virtue of any payment hereunder to a Party, shall be subrogated to such Party’s claim against Owner or any other Person relating thereto; provided, however, that the Guarantor shall not be entitled to receive payment from Owner in respect of any claim against Owner arising from a payment by the Guarantor in the event of any insolvency, bankruptcy, liquidation, reorganization or other similar proceedings relating to Owner, or in the event of any proceedings for voluntary liquidation, dissolution or other winding-up of Owner, whether or not involving insolvency or bankruptcy proceedings, in which case the Guaranteed Obligations shall be paid and performed in full before any payment in respect of a claim by the Guarantor shall be made by or on behalf of Owner.

Section 4. Amendments, Etc. No amendment of or supplement to this Guarantee, or waiver or modification of, or consent under, the terms hereof, shall be effective unless evidenced by an instrument in writing signed by the Guarantor and each Party against whom such amendment, supplement, waiver, modification or consent is to be enforced.

Section 5. Payments. All payments by the Guarantor hereunder in respect of any Obligation shall be made in Dollars and otherwise as provided in the relevant Indenture, the relevant Participation Agreement or the relevant Equipment Note in which such Guaranteed Obligation is contained.

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Section 6. Integration; Counterparts; Successors and Assigns; Headings. This Guarantee (a) constitutes the entire agreement, and supersedes all prior agreements and understandings, both written and oral, among the Guarantor and the Parties, with respect to the subject matter hereof, (b) may be executed in several counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument, and (c) shall be binding upon the successors and assigns of the Guarantor and shall inure to the benefit of, and shall be enforceable by, each of the Parties to the fullest extent permitted by applicable laws. The headings in this Guarantee are for purposes of reference only, and shall not limit or otherwise affect the meanings hereof.

Section 7. Notices. All requests, notices or other communications hereunder shall be in writing, addressed as follows:

If to the Guarantor:

UAL Corporation

77 West Wacker Drive

Chicago, Illinois 60601

Attention: Kathryn A. Mikells, Executive Vice President & Chief Financial Officer

Facsimile: (312)  ###-###-####

with a copy to:

77 West Wacker Drive

Chicago, Illinois 60601

Attention: General Counsel

Facsimile: (312)  ###-###-####

If to a Party:

to the address or telecopy number set forth in the Participation Agreements

All requests, notices or other communications shall be given in the manner, and shall be effective at the times and under the terms, set forth in Section 11.7 of the Participation Agreements.

Section 8. No Waivers. No failure on the part of any Party to exercise, no delay in exercising, and no course of dealing with respect to, any right or remedy hereunder will operate as a waiver thereof; nor will any single or partial exercise of any right or remedy hereunder preclude any other or further exercise of such right or remedy or the exercise of any other right or remedy.

Section 9. Severability. To the fullest extent permitted by applicable law, any provision of this Guarantee that is prohibited or unenforceable in any jurisdiction shall, as to such jurisdiction, be ineffective to the extent of such prohibition or unenforceability without invalidating the remaining provisions hereof or any provision in any other Operative Document, and any such prohibition or unenforceability in any jurisdiction shall not invalidate or render unenforceable such provision in any other jurisdiction.

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Section 10. GOVERNING LAW. THIS GUARANTEE SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK, (WITHOUT REGARD TO PRINCIPLES OF CONFLICTS OF LAWS THEREOF (OTHER THAN SECTIONS 5-1401 AND 5-1402 OF THE NEW YORK GENERAL OBLIGATIONS LAW)). THIS GUARANTEE IS BEING DELIVERED IN NEW YORK, NEW YORK.

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IN WITNESS WHEREOF, the undersigned has caused this Guarantee to be duly executed as of the day and year first written above.

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SCHEDULE I

TO GUARANTEE

PARTIES

Wilmington Trust Company, as Loan Trustee

Wilmington Trust Company, as Pass Through Trustee

Wilmington Trust Company, as Subordination Agent

SCHEDULE I

Page 1

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SCHEDULE II

TO GUARANTEE

AIRCRAFT

SCHEDULE II

Page 1

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SCHEDULE II

Page 2