<PAGE>
                                                                     EXHIBIT 4.5







                         TRUST SUPPLEMENT No. 2001-1A-2

                             Dated October   , 2001


                                     between

                            WILMINGTON TRUST COMPANY
                                   as Trustee,


                                       and


                             SOUTHWEST AIRLINES CO.

                                       to

                          PASS THROUGH TRUST AGREEMENT
                          Dated as of October 10, 2001


                                  $375,000,000

                 Southwest Airlines Pass Through Trust 2001-1A-2
                            5.496% Southwest Airlines
                           Pass Through Certificates,
                                Series 2001-1A-2



<PAGE>

                  This Trust Supplement No. 2001-1A-2, dated as of October   ,
2001 (herein called the "Trust Supplement"), between Southwest Airlines Co., a
Texas corporation (the "Company"), and Wilmington Trust Company (the "Trustee"),
to the Pass Through Trust Agreement, dated as of October 10, 2001, between the
Company and the Trustee (the "Basic Agreement").


                                   WITNESSETH:

                  WHEREAS, the Basic Agreement, unlimited as to the aggregate
principal amount of Certificates (unless otherwise specified herein, capitalized
terms used herein without definition having the respective meanings specified in
the Basic Agreement) which may be issued thereunder, has heretofore been
executed and delivered;

                  WHEREAS, pursuant to each Indenture, the Company proposes to
issue, on a recourse basis, Equipment Notes each secured by one of 29 aircraft
(each, an "Aircraft") owned by the Company;

                  WHEREAS, the Trustee hereby declares the creation of this
Southwest Airlines Pass Through Trust 2001-1A-2 (the "Applicable Trust") for the
benefit of the Applicable Certificateholders, and the initial Applicable
Certificateholders as the grantors of the Applicable Trust, by their respective
acceptances of the Applicable Certificates, join in the creation of the
Applicable Trust with the Trustee;

                  WHEREAS, all Certificates to be issued by the Applicable Trust
will evidence fractional undivided interests in the Applicable Trust and will
convey no rights, benefits or interests in respect of any property other than
the Trust Property;

                  WHEREAS, pursuant to the terms and conditions of the Basic
Agreement as supplemented by this Trust Supplement (the "Agreement") and each
Participation Agreement, the Trustee on behalf of the Applicable Trust (using a
portion of the proceeds from the sale of the Applicable Certificates, shall
purchase one or more Equipment Notes having the same interest rate as, and final
maturity date not later than the final Regular Distribution Date of, the
Applicable Certificates issued hereunder and shall hold such Equipment Notes in
trust for the benefit of the Applicable Certificateholders;

                  WHEREAS, all of the conditions and requirements necessary to
make this Trust Supplement, when duly executed and delivered, a valid, binding
and legal instrument in accordance with its terms and for the purposes herein
expressed, have been done, performed and fulfilled, and the execution and
delivery of this Trust Supplement in the form and with the terms hereof have
been in all respects duly authorized;

                  WHEREAS, this Trust Supplement is subject to the provisions of
the Trust Indenture Act of 1939, as amended, and shall, to the extent
applicable, be governed by such provisions;



<PAGE>
                                       2


                  NOW THEREFORE, in consideration of the premises herein, it is
agreed between the Company and the Trustee as follows:


                                    ARTICLE I
                                THE CERTIFICATES

                  Section 1.01. The Certificates. There is hereby created a
series of Certificates to be issued under the Agreement to be distinguished and
known as "5.496% Southwest Airlines Pass Through Certificates, Series 2001-1A-2"
(hereinafter defined as the "Applicable Certificates"). Each Applicable
Certificate represents a fractional undivided interest in the Applicable Trust
created hereby. The Applicable Certificates shall be the only instruments
evidencing a fractional undivided interest in the Applicable Trust.

                  The terms and conditions applicable to the Applicable
Certificates are as follows:

                  (a) The aggregate principal amount of the Applicable
         Certificates that shall be authenticated under the Agreement (except
         for Applicable Certificates authenticated and delivered pursuant to
         Sections 3.03, 3.04, 3.05 and 3.06 of the Basic Agreement) is
         $375,000,000.

                  (b) The Regular Distribution Dates with respect to any payment
         of Scheduled Payments means May 1 and November 1 of each year,
         commencing on May 1, 2002, until payment of all of the Scheduled
         Payments to be made under the Equipment Notes has been made.

                  (c) The Special Distribution Dates with respect to the
         Applicable Certificates means any Business Day on which a Special
         Payment is to be distributed pursuant to the Agreement.

                  (d) The Applicable Certificates shall be in the form attached
         hereto as Exhibit A. Any Person acquiring or accepting an Applicable
         Certificate or an interest therein will, by such acquisition or
         acceptance, be deemed to represent and warrant to and for the benefit
         of each Owner Participant and the Company that either (i) the assets of
         an employee benefit plan subject to Title I of the Employee Retirement
         Income Security Act of 1974, as amended ("ERISA"), or of a plan subject
         to Section 4975 of the Internal Revenue Code of 1986, as amended (the
         "Code"), have not been used to purchase Applicable Certificates or an
         interest therein or (ii) the purchase and holding of Applicable
         Certificates or an interest therein is exempt from the prohibited
         transaction restrictions of ERISA and the Code pursuant to one or more
         prohibited transaction statutory or administrative exemptions.

                  (e) The Applicable Certificates shall be Book-Entry
         Certificates and shall be subject to the conditions set forth in the
         Letter of Representations between the Company and the Clearing Agency
         attached hereto as Exhibit B.


<PAGE>
                                       3


                  (f) The "Participation Agreements" as defined in this Trust
         Supplement are the "Note Purchase Agreements" referred to in the Basic
         Agreement.

                  (g) The Applicable Certificates are subject to the
         Intercreditor Agreement.

                  (h) The Applicable Certificates are entitled to the benefits
         of the Liquidity Facility.

                  (i) The Responsible Party is the Company.

                  (j) The date referred to in clause (i) of the definition of
         the term "PTC Event of Default" in the Basic Agreement is the Final
         Maturity Date.

                  (k) The "particular sections of the Note Purchase Agreement",
         for purposes of clause (3) of Section 7.07 of the Basic Agreement, are
         Section 8.1 of each Participation Agreement.

                  (l) The Equipment Notes to be acquired and held in the
         Applicable Trust, and the related Aircraft and Note Documents, are
         described in the related Participation Agreement.


                                   ARTICLE II
                                   DEFINITIONS

                  Section 2.01. Definitions. For all purposes of the Basic
Agreement as supplemented by this Trust Supplement, the following capitalized
terms have the following meanings (any term used herein which is defined in both
this Trust Supplement and the Basic Agreement shall have the meaning assigned
thereto in this Trust Supplement for purposes of the Basic Agreement as
supplemented by this Trust Supplement):

                  Agreement: Has the meaning specified in the recitals hereto.

                  Aircraft: Means each of the Aircraft in respect of which a
         Participation Agreement is entered into on the date hereof (or any
         substitute aircraft, including engines therefor, owned by Company and
         securing one or more Equipment Notes).

                  Applicable Certificate: Has the meaning specified in Section
         1.01 of this Trust Supplement.

                  Applicable Certificateholder: Means the Person in whose name
         an Applicable Certificate is registered on the Register for the
         Applicable Certificates.

                  Applicable Participation Agreement: Has the meaning specified
         in Section 5.01(b) of this Trust Supplement.


<PAGE>
                                       4


                  Applicable Trust: Has the meaning specified in the recitals
         hereto.

                  Basic Agreement: Has the meaning specified in the first
         paragraph of this Trust Supplement.

                  Business Day: Means any day other than a Saturday, a Sunday or
         a day on which commercial banks are required or authorized to close in
         Dallas, Texas, New York, New York, Wilmington, Delaware or, so long as
         any Applicable Certificate is Outstanding, the city and state in which
         the Trustee or any Loan Trustee maintains its Corporate Trust Office or
         receives and disburses funds.

                  Certificates: Means the certificates issued by the Other
         Trusts.

                  Company: Has the meaning specified in the first paragraph of
         this Trust Supplement.

                  Controlling Party: Has the meaning specified in the
         Intercreditor Agreement.

                  Cut-off Date: Means the earlier of (a) November 30, 2001 and
         (b) the date on which a Triggering Event occurs.

                  Distribution Date: Means any Regular Distribution Date or
         Special Distribution Date as the context requires.

                  Final Maturity Date: Means May 1, 2008.

                  Indenture: Means, with respect to the Equipment Notes, each of
         the separate trust indentures and mortgages relating to the Aircraft,
         each as specified or described in Schedule I attached to the
         Intercreditor Agreement.

                  Intercreditor Agreement: Means the Intercreditor Agreement
         dated as of October 30, 2001 among the Trustee, the Other Trustees, the
         Liquidity Provider, the liquidity providers relating to the
         Certificates issued under each of the Other Agreements, and Wilmington
         Trust Company, as Subordination Agent and as trustee thereunder, as
         amended, supplemented or otherwise modified from time to time in
         accordance with its terms.

                  Investors: Means the Underwriters together with all subsequent
         beneficial owners of the Applicable Certificates.

                  Liquidity Facility: Means, initially, the Revolving Credit
         Agreement dated as of October 30, 2001 relating to the Applicable
         Certificates, between the Liquidity Provider and Wilmington Trust
         Company, as Subordination Agent, as agent and trustee for the
         Applicable Trust, and, from and after the replacement of such agreement
         pursuant to the Intercreditor Agreement, the replacement liquidity
         facility therefor, in each case as


<PAGE>
                                       5


         amended, supplemented or otherwise modified from time to time in
         accordance with their respective terms.

                  Liquidity Provider: Means, initially, Westdeutsche Landesbank
         Girozentrale, acting through its New York Branch, and any replacements
         or successors therefor appointed in accordance with the Intercreditor
         Agreement.

                  Note Documents: Means the Equipment Notes with respect to the
         Applicable Certificates and, with respect to any such Equipment Note,
         (i) the Indenture and the Participation Agreement relating to such
         Equipment Note.

                  Other Agreements: Means (i) the Basic Agreement as
         supplemented by Trust Supplement No. 2001-1A-1 dated the date hereof
         relating to Southwest Airlines Pass Through Trust 2001-1A-1 and (ii)
         the Basic Agreement as supplemented by Trust Supplement No. 2001-1B
         dated the date hereof relating to Southwest Airlines Pass Through Trust
         2001-1B.

                  Other Trustees: Means the trustees under the Other Agreements,
         and any successor or other trustee appointed as provided therein.

                  Other Trusts: Means the Southwest Airlines Pass Through Trust
         2001-1A-1 and the Southwest Airlines Pass Through Trust 2001-1B,
         created by the Other Agreements.

                  Participation Agreement: With respect to any Aircraft, means
         the Participation Agreement referred to in the related Indenture.

                  Pool Balance: Means, as of any date, (i) the original
         aggregate face amount of the Applicable Certificates less (ii) the
         aggregate amount of all payments made in respect of such Applicable
         Certificates other than payments made in respect of interest or premium
         thereon or reimbursement of any costs or expenses incurred in
         connection therewith. The Pool Balance as of any Distribution Date
         shall be computed after giving effect to any payment of principal of
         the Equipment Notes or payment with respect to other Trust Property and
         the distribution thereof to be made on that date.

                  Pool Factor: Means, as of any Distribution Date, the quotient
         (rounded to the seventh decimal place) computed by dividing (i) the
         Pool Balance by (ii) the original aggregate face amount of the
         Applicable Certificates.

                  Prospectus Supplement: Means the final Prospectus Supplement
         dated October 18, 2001 relating to the offering of the Applicable
         Certificates and the Certificates issued under the Other Agreements.

                  Ratings Confirmation: Has the meaning specified in the
         Intercreditor Agreement.


<PAGE>
                                       6


                  Special Payment: Means any payment (other than a Scheduled
         Payment) in respect of, or any proceeds of, any Equipment Note or
         Collateral (as defined in each Indenture).

                  Triggering Event: Has the meaning assigned to such term in the
         Intercreditor Agreement.

                  Trust Property: Means (i) subject to the Intercreditor
         Agreement, the Equipment Notes held as the property of the Applicable
         Trust, all monies at any time paid thereon and all monies due and to
         become due thereunder, (ii) funds from time to time deposited in the
         Certificate Account and the Special Payments Account and, subject to
         the Intercreditor Agreement, any proceeds from the sale of any
         Equipment Note by the Trustee pursuant to Article VI of the Basic
         Agreement and (iii) all rights of the Applicable Trust and the Trustee,
         on behalf of the Applicable Trust, under the Intercreditor Agreement,
         the Indentures, the Participation Agreements and the Liquidity
         Facility, including, without limitation, all rights to receive certain
         payments thereunder, and all monies paid to the Trustee on behalf of
         the Applicable Trust pursuant to the Intercreditor Agreement or the
         Liquidity Facility.

                  Trust Supplement: Has the meaning specified in the first
         paragraph of this trust supplement.

                  Underwriters: Means, collectively, Salomon Smith Barney Inc.,
         J.P. Morgan Securities Inc. and Merrill Lynch, Pierce, Fenner & Smith
         Incorporated.

                  Underwriting Agreement: Means the Underwriting Agreement dated
         October 18, 2001 among the Underwriters and the Company, as the same
         may be amended, supplemented or otherwise modified from time to time in
         accordance with its terms.

                                   ARTICLE III
                 DISTRIBUTIONS; STATEMENTS TO CERTIFICATEHOLDERS

                  Section 3.01. Statements to Applicable Certificateholders. (a)
On each Distribution Date, the Trustee will include with each distribution to
Applicable Certificateholders of a Scheduled Payment or Special Payment, as the
case may be, a statement setting forth the information provided below. Such
statement shall set forth (per $1,000 face amount Applicable Certificate as to
(ii) and (iii) below) the following information:

                  (i) the aggregate amount of funds distributed on such
         Distribution Date under the Agreement, including any portion thereof
         paid by the Liquidity Provider;

                  (ii) the amount of such distribution under the Agreement
         allocable to principal and the amount allocable to premium, if any;

                  (iii) the amount of such distribution under the Agreement
         allocable to interest; and


<PAGE>
                                       7


                  (iv) the Pool Balance and the Pool Factor.

                  With respect to the Applicable Certificates registered in the
name of a Clearing Agency, on the Record Date prior to each Distribution Date,
the Trustee will request from such Clearing Agency a securities position listing
setting forth the names of all Clearing Agency Participants reflected on such
Clearing Agency's books as holding interests in the Applicable Certificates on
such Record Date. On each Distribution Date, the Trustee will mail to each such
Clearing Agency Participant the statement described above and will make
available additional copies as requested by such Clearing Agency Participant for
forwarding to holders of interests in the Applicable Certificates.

                  (b) Within a reasonable period of time after the end of each
calendar year but not later than the latest date permitted by law, the Trustee
shall furnish to each Person who at any time during such calendar year was an
Applicable Certificateholder of record a statement containing the sum of the
amounts determined pursuant to clauses (a)(i), (a)(ii) and (a)(iii) above for
such calendar year or, in the event such Person was an Applicable
Certificateholder of record during a portion of such calendar year, for such
portion of such year, and such other items as are readily available to the
Trustee and which an Applicable Certificateholder shall reasonably request as
necessary for the purpose of such Applicable Certificateholder's preparation of
its federal income tax returns. Such statement and such other items shall be
prepared on the basis of information supplied to the Trustee by the Clearing
Agency Participants and shall be delivered by the Trustee to such Clearing
Agency Participants to be available for forwarding by such Clearing Agency
Participants to the holders of interests in the Applicable Certificates in the
manner described in Section 3.01(a) of this Trust Supplement.

                  (c) Promptly following the date of any early redemption or
purchase of, or any default in the payment of principal or interest in respect
of, any of the Equipment Notes held in the Applicable Trust, the Trustee shall
furnish to Applicable Certificateholders of record on such date a statement
setting forth (x) the expected Pool Balances for each subsequent Regular
Distribution Date, (y) the related Pool Factors for such Regular Distribution
Dates and (z) the expected principal distribution schedule of the Equipment
Notes, in the aggregate, held as Trust Property at the date of such notice.

                  (d) This Section 3.01 supersedes and replaces Section 4.03 of
the Basic Agreement, with respect to the Applicable Trust.

                  Section 3.02. Special Payments Account. (a) The Trustee shall
establish and maintain on behalf of the Applicable Certificateholders a Special
Payments Account as one or more accounts, which shall be non-interest bearing
except as provided in Section 4.04 of the Basic Agreement. The Trustee shall
hold the Special Payments Account in trust for the benefit of the Applicable
Certificateholders and shall make or permit withdrawals therefrom only as
provided in the Agreement. On each day when one or more Special Payments are
made to the Trustee under the Intercreditor Agreement, the Trustee, upon receipt
thereof, shall immediately deposit the aggregate amount of such Special Payments
in the Special Payments Account.


<PAGE>
                                       8


                  (b) This Section 3.02 supersedes and replaces Section 4.01(b)
of the Basic Agreement in its entirety, with respect to the Applicable Trust.

                  Section 3.03. Distributions from Special Payments Account. (a)
On each Special Distribution Date with respect to any Special Payment or as soon
thereafter as the Trustee has confirmed receipt of any Special Payments due on
the Equipment Notes held (subject to the Intercreditor Agreement) in the
Applicable Trust or realized upon the sale of such Equipment Notes, the Trustee
shall distribute out of the Special Payments Account the entire amount of such
Special Payment deposited therein pursuant to Section 3.02(a) of this Trust
Supplement. There shall be so distributed to each Applicable Certificateholder
of record on the Record Date with respect to such Special Distribution Date
(other than as provided in Section 7.01 of this Trust Supplement concerning the
final distribution) by check mailed to such Applicable Certificateholder, at the
address appearing in the Register, such Applicable Certificateholder's pro rata
share (based on the Fractional Undivided Interest in the Applicable Trust held
by such Applicable Certificateholder) of the total amount in the Special
Payments Account on account of such Special Payment, except that, with respect
to Applicable Certificates registered on the Record Date in the name of a
Clearing Agency (or its nominee), such distribution shall be made by wire
transfer in immediately available funds to the account designated by such
Clearing Agency (or such nominee).

                  (b) The Trustee shall, at the expense of the Company, cause
notice of each Special Payment to be mailed to each Applicable Certificateholder
at his address as it appears in the Register. In the event of redemption or
purchase of Equipment Notes held in the Applicable Trust, such notice shall be
mailed not less than 15 days prior to the Special Distribution Date for the
Special Payment resulting from such redemption or purchase, which Special
Distribution Date shall be the date of such redemption or purchase. Such notice
shall be mailed as soon as practicable after the Trustee has confirmed that it
has received funds for such Special Payment, stating the Special Distribution
Date for such Special Payment which shall occur not less than 15 days after the
date of such notice and as soon as practicable thereafter. Notices mailed by the
Trustee shall set forth:

                  (i) the Special Distribution Date and the Record Date therefor
         (except as otherwise provided in Section 7.01 of this Trust
         Supplement),

                  (ii) the amount of the Special Payment for each $1,000 face
         amount Applicable Certificate and the amount thereof constituting
         principal, premium, if any, and interest,

                  (iii) the reason for the Special Payment, and

                  (iv) if the Special Distribution Date is the same date as a
         Regular Distribution Date, the total amount to be received on such date
         for each $1,000 face amount Applicable Certificate.

If the amount of premium, if any, payable upon the redemption or purchase of an
Equipment Note has not been calculated at the time that the Trustee mails notice
of a Special Payment, it


<PAGE>
                                       9


shall be sufficient if the notice sets forth the other amounts to be distributed
and states that any premium received will also be distributed.

                  If any redemption of the Equipment Notes held in the Trust is
canceled, the Trustee, as soon as possible after learning thereof, shall cause
notice thereof to be mailed to each Applicable Certificateholder at its address
as it appears on the Register.

                  (c) This Section 3.03 supersedes and replaces Section 4.02(b)
and Section 4.02(c) of the Basic Agreement in their entirety, with respect to
the Applicable Trust.

                                   ARTICLE IV
                                     DEFAULT

                  Section 4.01. Purchase Rights of Certificateholders. (a) At
any time after the occurrence and during the continuation of a Triggering Event,
if the Class A-1 Trustee is then the Controlling Party, each Applicable
Certificateholder shall have the right to purchase, for the purchase price set
forth in the Class A-1 Trust Agreement, all, but not less than all, of the Class
A-1 Certificates upon ten days' written notice to the Class A-1 Trustee and each
other Applicable Certificateholder, provided that (i) if prior to the end of
such ten-day period any other Applicable Certificateholder notifies such
purchasing Applicable Certificateholder that such other Applicable
Certificateholder wants to participate in such purchase, then such other
Applicable Certificateholder may join with the purchasing Applicable
Certificateholder to purchase all, but not less than all, of the Class A-1
Certificates pro rata based on the Fractional Undivided Interest in the
Applicable Trust held by each such Applicable Certificateholder and (ii) if
prior to the end of such ten-day period any other Applicable Certificateholder
fails to notify the purchasing Applicable Certificateholder of such other
Applicable Certificateholder's desire to participate in such a purchase, then
such other Applicable Certificateholder shall lose its right to purchase the
Class A-1 Certificates pursuant to this Section 4.01(a).

                  (b) By acceptance of its Applicable Certificate, each
Applicable Certificateholder agrees that at any time after the occurrence and
during the continuation of a Triggering Event,

                  (i) if the Trustee is then the Controlling Party, each Class
         A-1 Certificateholder shall have the right to purchase all, but not
         less than all, of the Applicable Certificates upon ten days' written
         notice to the Trustee and each other Class A-1 Certificateholder,
         provided that (A) if prior to the end of such ten-day period any other
         Class A-1 Certificateholder notifies such purchasing Class A-1
         Certificateholder that such other Class A-1 Certificateholder wants to
         participate in such purchase, then such other Class A-1
         Certificateholder may join with the purchasing Class A-1
         Certificateholder to purchase all, but not less than all, of the
         Applicable Certificates pro rata based on the Fractional Undivided
         Interest in the Class A-1 Trust held by each such Class A-1
         Certificateholder and (B) if prior to the end of such ten-day period
         any other Class A-1 Certificateholder fails to notify the purchasing
         Class A-1 Certificateholder of such other Class A-1 Certificateholder's
         desire to participate in such a purchase, then such other Class A-1
         Certificateholder shall lose its right to purchase the Applicable
         Certificates pursuant to this Section 4.01(b);


<PAGE>
                                       10


                  (ii) each Class B Certificateholder shall have the right
         (which shall not expire upon any purchase of the Applicable
         Certificates pursuant to clause (a) or (b)(i) above) to purchase all,
         but not less than all, of the Applicable Certificates and the Class A-1
         Certificates upon ten days' written notice to the Trustee, the Class
         A-1 Trustee and each other Class B Certificateholder, provided that (A)
         if prior to the end of such ten-day period any other Class B
         Certificateholder notifies such purchasing Class B Certificateholder
         that such other Class B Certificateholder wants to participate in such
         purchase, then such other Class B Certificateholder may join with the
         purchasing Class B Certificateholder to purchase all, but not less than
         all, of the Applicable Certificates and the Class A-1 Certificates pro
         rata based on the Fractional Undivided Interest in the Class B Trust
         held by each such Class B Certificateholder and (B) if prior to the end
         of such ten-day period any other Class B Certificateholder fails to
         notify the purchasing Class B Certificateholder of such other Class B
         Certificateholder's desire to participate in such a purchase, then such
         other Class B Certificateholder shall lose its right to purchase the
         Applicable Certificates and the Class A-1 Certificates pursuant to this
         Section 4.01(b); and

                  (iii) each holder of a Class C Certificate (a "Class C
         Certificateholder") shall have the right (which shall not expire upon
         any purchase of the Applicable Certificates pursuant to clause (a),
         (b)(i) or (b)(ii) above) to purchase all, but not less than all, of the
         Applicable Certificates, the Class A-1 Certificates and the Class B
         Certificates upon ten days' written notice to the Trustee, the Class
         A-1 Trustee, the Class B Trustee and each other Class C
         Certificateholder, provided that (A) if prior to the end of such
         ten-day period any other Class C Certificateholder notifies such
         purchasing Class C Certificateholder that such other Class C
         Certificateholder wants to participate in such purchase, then such
         other Class C Certificateholder may join with the purchasing Class C
         Certificateholder to purchase all, but not less than all, of the
         Applicable Certificates, the Class A-1 Certificates and the Class B
         Certificates pro rata based on the Fractional Undivided Interest in the
         Class C Trust held by each such Class C Certificateholder and (B) if
         prior to the end of such ten-day period any other Class C
         Certificateholder fails to notify the purchasing Class C
         Certificateholder of such other Class C Certificateholder's desire to
         participate in such a purchase, then such other Class C
         Certificateholder shall lose its right to purchase the Applicable
         Certificates, the Class A-2 Certificates and the Class B Certificates
         pursuant to this Section 4.01(b).

                  The purchase price with respect to the Applicable Certificates
shall be equal to the Pool Balance of the Applicable Certificates, together with
accrued and unpaid interest thereon to the date of such purchase, without
premium, but including any other amounts then due and payable to the Applicable
Certificateholders under the Agreement, the Intercreditor Agreement or any Note
Document or on or in respect of the Applicable Certificates; provided, however,
that no such purchase of Applicable Certificates shall be effective unless the
purchaser(s) shall certify to the Trustee that contemporaneously with such
purchase, such purchaser(s) is (are) purchasing, pursuant to the terms of the
Agreement and the Other Agreements, (A) in the case of any purchase of the
Applicable Certificates pursuant to clause (b)(i) above, all of the Applicable
Certificates, or (B) in all other cases, the Applicable Certificates, the Class
A-1 Certificates and the Class B Certificates that are senior to the securities
held by such purchaser(s). Each payment


<PAGE>
                                       11


of the purchase price of the Applicable Certificates referred to in the first
sentence hereof shall be made to an account or accounts designated by the
Trustee and each such purchase shall be subject to the terms of this Section
4.01(b). Each Applicable Certificateholder agrees by its acceptance of its
Applicable Certificate that (at any time after the occurrence and during the
continuation of a Triggering Event) it will, upon payment from such Class A-1
Certificateholder(s), Class B Certificateholder(s), or Class C
Certificateholder(s), as the case may be, of the purchase price set forth in the
first sentence of this paragraph, (i) forthwith sell, assign, transfer and
convey to the purchaser(s) thereof (without recourse, representation or warranty
of any kind except for its own acts), all of the right, title, interest and
obligation of such Applicable Certificateholder in the Agreement, the
Intercreditor Agreement, the Liquidity Facility, the Note Documents and all
Applicable Certificates held by such Applicable Certificateholder (excluding all
right, title and interest under any of the foregoing to the extent such right,
title or interest is with respect to an obligation not then due and payable as
respects any action or inaction or state of affairs occurring prior to such
sale) (and the purchaser shall assume all of such Applicable Certificateholder's
obligations under the Agreement, the Intercreditor Agreement, the Liquidity
Facility, the Note Documents and all such Applicable Certificates and (ii) if
such purchase occurs after a Record Date relating to any distribution and prior
to or on the related Distribution Date, forthwith turn over to the purchaser(s)
of its Applicable Certificate all amounts, if any, received by it on account of
such distribution. The Applicable Certificates will be deemed to be purchased on
the date payment of the purchase price is made notwithstanding the failure of
the Applicable Certificateholders to deliver any Applicable Certificates and,
upon such a purchase, (I) the only rights of the Applicable Certificateholders
will be to deliver the Applicable Certificates to the purchaser(s) and receive
the purchase price for such Applicable Certificates and (II) if the purchaser(s)
shall so request, such Applicable Certificateholder will comply with all the
provisions of Section 3.04 of the Basic Agreement to enable new Applicable
Certificates to be issued to the purchaser in such denominations as it shall
request. All charges and expenses in connection with the issuance of any such
new Applicable Certificates shall be borne by the purchaser thereof.

                  As used in this Section 4.01 and elsewhere in this Trust
Supplement, the terms "Class A-1 Certificate", "Class A-1 Certificateholder",
"Class A-1 Trust", "Class A-1 Trust Agreement", "Class A-2 Trustee", "Class B
Certificate", "Class B Certificateholder", "Class B Trust", "Class B Trustee",
"Class C Certificate", "Class C Certificateholder" and "Class C Trust", shall
have the respective meanings assigned to such terms in the Intercreditor
Agreement.

                  (c) This Section 4.01 supersedes and replaces Section 6.01(b)
of the Basic Agreement, with respect to the Applicable Trust.

                  Section 4.02. Amendment of Section 6.05 of the Basic
Agreement. Section 6.05 of the Basic Agreement shall be amended, with respect to
the Applicable Trust, by deleting the phrase "and thereby annul any Direction
given by such Certificateholders or the Trustee to such Loan Trustee with
respect thereto," set forth in the first sentence thereof.


<PAGE>
                                       12


                                    ARTICLE V
                                   THE TRUSTEE

                  Section 5.01. Delivery of Documents; Delivery Dates. (a) The
Trustee is hereby directed (i) to execute and deliver the Intercreditor
Agreement, each Participation Agreement and each Indenture on or prior to the
Issuance Date, each in the form delivered to the Trustee by the Company, and
(ii) subject to the respective terms thereof, to perform its obligations
thereunder. Upon request of the Company and the satisfaction or waiver of the
closing conditions specified in the Underwriting Agreement, the Trustee shall
execute, deliver, authenticate, issue and sell Applicable Certificates in
authorized denominations equaling in the aggregate the amount set forth, with
respect to the Applicable Trust, in Schedule I to the Underwriting Agreement
evidencing the entire ownership interest in the Applicable Trust, which amount
equals the maximum aggregate principal amount of Equipment Notes which may be
purchased by the Trustee pursuant to the Participation Agreements. Except as
provided in Sections 3.03, 3.04, 3.05 and 3.06 of the Basic Agreement, the
Trustee shall not execute, authenticate or deliver Applicable Certificates in
excess of the aggregate amount specified in this paragraph. The provisions of
this Section 5.01(a) supersede and replace the first sentence of Section 3.02(a)
of the Basic Agreement, with respect to the Applicable Trust.

                  (b) On the Issuance Date, the Trustee shall, subject to the
conditions set forth in Section 4 of each Participation Agreement, perform its
obligations under the Participation Agreement (the "Applicable Participation
Agreement") and cause such certificates, documents and legal opinions relating
to the Trustee to be duly delivered as required by the Applicable Participation
Agreement. Upon satisfaction of the conditions specified in the Applicable
Participation Agreement, the Trustee shall purchase the applicable Equipment
Notes from a portion of the proceeds of the sale of the Applicable Certificates.
The purchase price of such Equipment Notes shall equal the principal amount of
such Equipment Notes.

                  (c) The Trustee acknowledges its acceptance of all right,
title and interest in and to the Trust Property to be acquired pursuant to
Section 5.01(b) of this Trust Supplement and each Applicable Participation
Agreement, and declares that it holds and will hold such right, title and
interest for the benefit of all present and future Applicable
Certificateholders, upon the trusts set forth in the Agreement. By its
acceptance of an Applicable Certificate, each initial Applicable
Certificateholder, as a grantor of the Applicable Trust, joins with the Trustee
in the creation of the Applicable Trust. The provisions of this Section 5.01(c)
supersede and replace the provisions of Section 2.03 of the Basic Agreement,
with respect to the Applicable Trust.

                  Section 5.02. The Trustee. (a) Subject to Section 5.03 of this
Trust Supplement and Section 7.15 of the Basic Agreement, the Trustee shall not
be responsible in any manner whatsoever for or in respect of the validity or
sufficiency of this Trust Supplement, or the Participation Agreements or the due
execution hereof or thereof by the Company or the other parties thereto (other
than the Trustee), or for or in respect of the recitals and statements contained
herein or therein, all of which recitals and statements are made solely by the
Company, except that the Trustee hereby represents and warrants that each of
this Trust Supplement, the Basic Agreement, each Applicable Certificate, the
Intercreditor Agreement and the Participation


<PAGE>
                                       13


Agreements has been executed and delivered by one of its officers who is duly
authorized to execute and deliver such document on its behalf.

                  (b) Except as herein otherwise provided and except during the
continuation of an Event of Default in respect of the Applicable Trust created
hereby, no duties, responsibilities or liabilities are assumed, or shall be
construed to be assumed, by the Trustee by reason of this Trust Supplement other
than as set forth in the Agreement and this Trust Supplement is executed and
accepted on behalf of the Trustee, subject to all the terms and conditions set
forth in the Agreement, as fully to all intents as if the same were herein set
forth at length.

                  Section 5.03. Representations and Warranties of the Trustee.
The Trustee hereby represents and warrants that:

                  (a) the Trustee has full power, authority and legal right to
         execute, deliver and perform this Trust Supplement, the Intercreditor
         Agreement and the Note Documents to which it is a party and has taken
         all necessary action to authorize the execution, delivery and
         performance by it of this Trust Supplement, the Intercreditor Agreement
         and the Note Documents to which it is a party;

                  (b) the execution, delivery and performance by the Trustee of
         this Trust Supplement, the Intercreditor Agreement and the Note
         Documents to which it is a party (i) will not violate any provision of
         any United States federal law or the law of the state of the United
         States where it is located governing the banking and trust powers of
         the Trustee or any order, writ, judgment, or decree of any court,
         arbitrator or governmental authority applicable to the Trustee or any
         of its assets, (ii) will not violate any provision of the articles of
         association or by-laws of the Trustee, and (iii) will not violate any
         provision of, or constitute, with or without notice or lapse of time, a
         default under, or result in the creation or imposition of any lien on
         any properties included in the Trust Property pursuant to the
         provisions of any mortgage, indenture, contract, agreement or other
         undertaking to which it is a party, which violation, default or lien
         could reasonably be expected to have an adverse effect on the Trustee's
         performance or ability to perform its duties hereunder or thereunder or
         on the transactions contemplated herein or therein;

                  (c) the execution, delivery and performance by the Trustee of
         this Trust Supplement, the Intercreditor Agreement and the Note
         Documents to which it is a party will not require the authorization,
         consent, or approval of, the giving of notice to, the filing or
         registration with, or the taking of any other action in respect of, any
         governmental authority or agency of the United States or the state of
         the United States where it is located regulating the banking and
         corporate trust activities of the Trustee; and

                  (d) this Trust Supplement, the Intercreditor Agreement and the
         Note Documents to which it is a party have been, or will be, as
         applicable, duly executed and delivered by the Trustee and constitute,
         or will constitute, as applicable, the legal, valid and binding
         agreements of the Trustee, enforceable against it in accordance with
         their respective terms; provided, however, that enforceability may be
         limited by (i) applicable


<PAGE>
                                       14


         bankruptcy, insolvency, reorganization, moratorium or similar laws
         affecting the rights of creditors generally and (ii) general principles
         of equity.

                  Section 5.04. Trustee Liens. The Trustee in its individual
capacity agrees, in addition to the agreements contained in Section 7.17 of the
Basic Agreement, that it will at its own cost and expense promptly take any
action as may be necessary to duly discharge and satisfy in full any Trustee's
Liens on or with respect to the Trust Property which is attributable to the
Trustee in its individual capacity and which is unrelated to the transactions
contemplated by the Intercreditor Agreement or the Participation Agreements.


                                   ARTICLE VI
                  ADDITIONAL AMENDMENT; SUPPLEMENTAL AGREEMENTS

                  Section 6.01. [Reserved]

                  Section 6.02. Supplemental Agreements Without Consent of
Applicable Certificateholders. Without limitation of Section 9.01 of the Basic
Agreement, under the terms of, and subject to the limitations contained in,
Section 9.01 of the Basic Agreement, the Company may (but will not be required
to), and the Trustee (subject to Section 9.03 of the Basic Agreement) shall, at
the Company's request, at any time and from time to time, (i) enter into one or
more agreements supplemental to a Participation Agreement, for any of the
purposes set forth in clauses (1) through (9) of such Section 9.01, and (without
limitation of the foregoing or Section 9.01 of the Basic Agreement) (a) clauses
(2) and (3) of such Section 9.01 shall also be deemed to include the Company's
obligations under (in the case of clause (2)), and the Company's rights and
powers conferred by (in the case of clause (3)), the Participation Agreements,
and (b) references in clauses (4), (6) and (7) of such Section 9.01 to "any
Intercreditor Agreement or any Liquidity Facility" shall also be deemed to refer
to "the Intercreditor Agreement, the Liquidity Facility, or the Participation
Agreements and (ii) enter into one or more agreements supplemental to the
Agreement to provide for the formation of a Class C Trust, the issuance of Class
C Certificates, the purchase by the Class C Trust of Equipment Notes and other
matters incidental thereto or otherwise contemplated by Section 2.01(b) of the
Basic Agreement.

                  Section 6.03. Supplemental Agreements with Consent of
Applicable Certificateholders. Without limitation of Section 9.02 of the Basic
Agreement, the provisions of Section 9.02 of the Basic Agreement shall apply to
agreements or amendments for the purpose of adding any provisions to or changing
in any manner or eliminating any of the provisions of a Participation Agreement,
or modifying in any manner the rights and obligations of the Applicable
Certificateholders under a Participation Agreement.

                                   ARTICLE VII
                              TERMINATION OF TRUST

                  Section 7.01. Termination of the Applicable Trust. (a) The
respective obligations and responsibilities of the Company and the Trustee with
respect to the Applicable Trust shall


<PAGE>
                                       15


terminate upon the distribution to all Applicable Certificateholders and the
Trustee of all amounts required to be distributed to them pursuant to the
Agreement and the disposition of all property held as part of the Trust
Property; provided, however, that in no event shall the Applicable Trust
continue beyond one hundred ten (110) years following the date of the execution
of this Trust Supplement.

                  (b) In connection with the occurrence of the event set forth
in clause (a) above, notice of such termination, specifying the Distribution
Date upon which the Applicable Certificateholders may surrender their Applicable
Certificates to the Trustee for payment of the final distribution and
cancellation, shall be mailed promptly by the Trustee to Applicable
Certificateholders not earlier than the 60th day and not later than the 15th day
next preceding such final Distribution Date specifying (i) the Distribution Date
upon which the proposed final payment of the Applicable Certificates will be
made upon presentation and surrender of Applicable Certificates at the office or
agency of the Trustee therein specified, (ii) the amount of any such proposed
final payment, and (iii) that the Record Date otherwise applicable to such
Distribution Date is not applicable, payments being made only upon presentation
and surrender of the Applicable Certificates at the office or agency of the
Trustee therein specified. The Trustee shall give such notice to the Registrar
at the time such notice is given to Applicable Certificateholders. Upon
presentation and surrender of the Applicable Certificates in accordance with
such notice, the Trustee shall cause to be distributed to Applicable
Certificateholders such final payments.

                  In the event that all of the Applicable Certificateholders
shall not surrender their Applicable Certificates for cancellation within six
months after the date specified in the above-mentioned written notice, the
Trustee shall give a second written notice to the remaining Applicable
Certificateholders to surrender their Applicable Certificates for cancellation
and receive the final distribution with respect thereto. No additional interest
shall accrue on the Applicable Certificates after the Distribution Date
specified in the first written notice. In the event that any money held by the
Trustee for the payment of distributions on the Applicable Certificates shall
remain unclaimed for two years (or such lesser time as the Trustee shall be
satisfied, after sixty days' notice from the Company, is one month prior to the
escheat period provided under applicable law) after the final distribution date
with respect thereto, the Trustee shall pay to each Loan Trustee the appropriate
amount of money relating to such Loan Trustee and shall give written notice
thereof to the Company.

                  (c) The provisions of this Section 7.01 supersede and replace
the provisions of Section 11.01 of the Basic Agreement in its entirety, with
respect to the Applicable Trust.


                                  ARTICLE VIII
                            MISCELLANEOUS PROVISIONS

                  Section 8.01. Basic Agreement Ratified. Except and so far as
herein expressly provided, all of the provisions, terms and conditions of the
Basic Agreement are in all respects ratified and confirmed; and the Basic
Agreement and this Trust Supplement shall be taken, read and construed as one
and the same instrument. All replacements of provisions of, and other


<PAGE>
                                       16


modifications of the Basic Agreement set forth in this Trust Supplement are
solely with respect to the Applicable Trust.

                  SECTION 8.02. GOVERNING LAW. THE AGREEMENT AND THE APPLICABLE
CERTIFICATES SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF
THE STATE OF NEW YORK AND THE OBLIGATIONS, RIGHTS AND REMEDIES OF THE PARTIES
UNDER THIS AGREEMENT SHALL BE DETERMINED IN ACCORDANCE WITH SUCH LAWS.

                  Section 8.03. Execution in Counterparts. This Trust Supplement
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 8.04. Intention of Parties. The parties hereto intend
that the Applicable Trust be classified for U.S. federal income tax purposes as
a grantor trust under Subpart E, Part I of Subchapter J of the Internal Revenue
Code of 1986, as amended, and not as a trust or association taxable as a
corporation or as a partnership. Each Applicable Certificateholder and Investor,
by its acceptance of its Applicable Certificate or a beneficial interest
therein, agrees to treat the Applicable Trust as a grantor trust for all U.S.
federal, state and local income tax purposes. The powers granted and obligations
undertaken pursuant to the Agreement shall be so construed so as to further such
intent.


<PAGE>
                                       17


                  IN WITNESS WHEREOF, the Company and the Trustee have caused
this Trust Supplement to be duly executed by their respective officers thereto
duly authorized, as of the day and year first written above.

                                       SOUTHWEST AIRLINES CO.


                                       By:
                                          --------------------------------------
                                       Name: Laura Wright
                                       Title: Vice President-Finance and
                                              Treasurer



                                       WILMINGTON TRUST COMPANY,
                                            as Trustee


                                       By:
                                          --------------------------------------
                                       Name:
                                       Title:



<PAGE>

                                    EXHIBIT A


                               FORM OF CERTIFICATE

Certificate
No. __

                  Unless this certificate is presented by an authorized
representative of The Depository Trust Company, a New York corporation ("DTC"),
to Issuer or its agent for registration of transfer, exchange or payment, and
any certificate issued is registered in the name of Cede & Co. or in such other
name as is requested by an authorized representative of DTC (and any payment is
made to Cede & Co. or to such other entity as is requested by an authorized
representative of DTC), ANY TRANSFER, PLEDGE OR OTHER USE HEREOF FOR VALUE OR
OTHERWISE BY OR TO ANY PERSON IS WRONGFUL inasmuch the registered owner hereof,
Cede & Co., has an interest herein.



                 SOUTHWEST AIRLINES PASS THROUGH TRUST 2001-1A-2

      5.496% Southwest Airlines Pass Through Certificate, Series 2001-1A-2
                         Issuance Date: October 30, 2001

                        Final Maturity Date: May 1, 2008

Evidencing a fractional undivided interest in the Southwest Airlines Pass
Through Trust 2001-1A-2, the property of which shall include certain Equipment
Notes each secured by an Aircraft owned by Southwest Airlines Co.

                  Fractional Undivided Interest representing ___% of the Trust
                  per $1,000 face amount

                  THIS CERTIFIES THAT CEDE & CO., for value received, is the
registered owner of a Fractional Undivided Interest, having a face amount of
$_____ ( ____ Dollars), in the Southwest Airlines Pass Through Trust 2001-1A-2
(the "Trust") created by Wilmington Trust Company, as trustee (the "Trustee"),
pursuant to a Pass Through Trust Agreement, dated as of October 10, 2001 (the
"Basic Agreement"), between the Trustee and Southwest Airlines Co., a Delaware
corporation (the "Company"), as supplemented by Trust Supplement No. 2001-1A-2
thereto, dated as of October 30, 2001 (the "Trust Supplement" and, together with
the Basic Agreement, the "Agreement"), between the Trustee and the Company, a
summary of certain of the pertinent provisions of which is set forth below. To
the extent not otherwise defined herein, the capitalized terms used herein have
the meanings assigned to them in the Agreement. This Certificate is one of the
duly authorized Certificates designated as "5.496% Southwest Airlines Pass
Through Certificates, Series 2001-1A-2" (herein called the "Certificates"). This
Certificate


<PAGE>
                                      A-2


is issued under and is subject to the terms, provisions and conditions of the
Agreement. By virtue of its acceptance hereof, the holder of this Certificate
(the "Certificateholder" and, together with all other holders of Certificates
issued by the Trust, the "Certificateholders") assents to and agrees to be bound
by the provisions of the Agreement and the Intercreditor Agreement. The property
of the Trust includes certain Equipment Notes and all rights of the Trust to
receive payments under the Intercreditor Agreement and the Liquidity Facility
(the "Trust Property"). Each issue of the Equipment Notes is secured by, among
other things, a security interest in an Aircraft leased to or owned by the
Company.

                  The Certificates represent Fractional Undivided Interests in
the Trust and the Trust Property and have no rights, benefits or interest in
respect of any other separate trust established pursuant to the terms of the
Basic Agreement for any other series of certificates issued pursuant thereto.

                  Subject to and in accordance with the terms of the Agreement
and the Intercreditor Agreement, from funds then available to the Trustee, there
will be distributed on each May 1 and November 1 (a "Regular Distribution Date")
commencing May 1, 2002 to the Person in whose name this Certificate is
registered at the close of business on the 15th day preceding the Regular
Distribution Date, an amount in respect of the Scheduled Payments on the
Equipment Notes due on such Regular Distribution Date, the receipt of which has
been confirmed by the Trustee, equal to the product of the percentage interest
in the Trust evidenced by this Certificate and an amount equal to the sum of
such Scheduled Payments. Subject to and in accordance with the terms of the
Agreement and the Intercreditor Agreement, in the event that Special Payments on
the Equipment Notes are received by the Trustee, from funds then available to
the Trustee, there shall be distributed on the applicable Special Distribution
Date, to the Person in whose name this Certificate is registered at the close of
business on the 15th day preceding the Special Distribution Date, an amount in
respect of such Special Payments on the Equipment Notes, the receipt of which
has been confirmed by the Trustee, equal to the product of the percentage
interest in the Trust evidenced by this Certificate and an amount equal to the
sum of such Special Payments so received. If a Regular Distribution Date or
Special Distribution Date is not a Business Day, distribution shall be made on
the immediately following Business Day with the same force and effect as if made
on such Regular Distribution Date or Special Distribution Date and no interest
shall accrue during the intervening period. The Trustee shall mail notice of
each Special Payment and the Special Distribution Date therefor to the
Certificateholder of this Certificate.

                  Distributions on this Certificate will be made by the Trustee
by check mailed to the Person entitled thereto, without presentation or
surrender of this Certificate or the making of any notation hereon, except that
with respect to Certificates registered on the Record Date in the name of a
Clearing Agency (or its nominee), such distribution shall be made by wire
transfer. Except as otherwise provided in the Agreement and notwithstanding the
above, the final distribution on this Certificate will be made after notice
mailed by the Trustee of the pendency of such distribution and only upon
presentation and surrender of this Certificate at the office or agency of the
Trustee specified in such notice.


<PAGE>
                                      A-3


                  The Certificates do not represent a direct obligation of, or
an obligation guaranteed by, or an interest in, the Company or the Trustee or
any affiliate thereof. The Certificates are limited in right of payment, all as
more specifically set forth on the face hereof and in the Agreement. All
payments or distributions made to Certificateholders under the Agreement shall
be made only from the Trust Property and only to the extent that the Trustee
shall have sufficient income or proceeds from the Trust Property to make such
payments in accordance with the terms of the Agreement. Each Certificateholder
of this Certificate, by its acceptance hereof, agrees that it will look solely
to the income and proceeds from the Trust Property to the extent available for
distribution to such Certificateholder as provided in the Agreement. This
Certificate does not purport to summarize the Agreement and reference is made to
the Agreement for information with respect to the interests, rights, benefits,
obligations, privileges, and duties evidenced hereby. A copy of the Agreement
may be examined during normal business hours at the principal office of the
Trustee, and at such other places, if any, designated by the Trustee, by any
Certificateholder upon request.

                  The Agreement permits, with certain exceptions therein
provided, the amendment thereof and the modification of the rights and
obligations of the Company and the rights of the Certificateholders under the
Agreement at any time by the Company and the Trustee with the consent of the
Certificateholders holding Certificates evidencing Fractional Undivided
Interests aggregating not less than a majority in interest in the Trust. Any
such consent by the Certificateholder of this Certificate shall be conclusive
and binding on such Certificateholder and upon all future Certificateholders of
this Certificate and of any Certificate issued upon the transfer hereof or in
exchange hereof or in lieu hereof whether or not notation of such consent is
made upon this Certificate. The Agreement also permits the amendment thereof, in
certain limited circumstances, without the consent of the Certificateholders of
any of the Certificates.

                  As provided in the Agreement and subject to certain
limitations set forth therein, the transfer of this Certificate is registrable
in the Register upon surrender of this Certificate for registration of transfer
at the offices or agencies maintained by the Trustee in its capacity as
Registrar, or by any successor Registrar, duly endorsed or accompanied by a
written instrument of transfer in form satisfactory to the Trustee and the
Registrar, duly executed by the Certificateholder hereof or such
Certificateholder's attorney duly authorized in writing, and thereupon one or
more new Certificates of authorized denominations evidencing the same aggregate
Fractional Undivided Interest in the Trust will be issued to the designated
transferee or transferees.

                  The Certificates are issuable only as registered Certificates
without coupons in minimum denominations of $1,000 Fractional Undivided Interest
and integral multiples thereof except that one Certificate may be issued in a
different denomination. As provided in the Agreement and subject to certain
limitations therein set forth, the Certificates are exchangeable for new
Certificates of authorized denominations evidencing the same aggregate
Fractional Undivided Interest in the Trust, as requested by the
Certificateholder surrendering the same.

                  No service charge will be made for any such registration of
transfer or exchange, but the Trustee shall require payment of a sum sufficient
to cover any tax or governmental charge payable in connection therewith.


<PAGE>
                                      A-4


                  Each Certificateholder and Investor, by its acceptance of this
Certificate or a beneficial interest herein, agrees to treat the Trust as a
grantor trust for all U.S. federal, state and local income tax purposes.

                  The Trustee, the Registrar, and any agent of the Trustee or
the Registrar may treat the person in whose name this Certificate is registered
as the owner hereof for all purposes, and neither the Trustee, the Registrar,
nor any such agent shall be affected by any notice to the contrary.

                  The obligations and responsibilities created by the Agreement
and the Trust created thereby shall terminate upon the distribution to
Certificateholders of all amounts required to be distributed to them pursuant to
the Agreement and the disposition of all property held as part of the Trust
Property.

                  Any Person acquiring or accepting this Certificate or an
interest herein will, by such acquisition or acceptance, be deemed to have
represented and warranted to and for the benefit of the Company that either: (i)
the assets of an employee benefit plan subject to Title I of the Employee
Retirement Income Security Act of 1974, as amended ("ERISA"), or of a plan
subject to Section 4975 of the Internal Revenue Code of 1986, as amended (the
"Code"), have not been used to purchase this Certificate or an interest herein
or (ii) the purchase and holding of this Certificate or an interest herein are
exempt from the prohibited transaction restrictions of ERISA and the Code
pursuant to one or more prohibited transaction statutory or administrative
exemptions.

                  THE AGREEMENT AND THIS CERTIFICATE SHALL BE GOVERNED BY AND
CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK AND THE
OBLIGATIONS, RIGHTS AND REMEDIES OF THE PARTIES UNDER THIS AGREEMENT SHALL BE
DETERMINED IN ACCORDANCE WITH SUCH LAWS.

                  Unless the certificate of authentication hereon has been
executed by the Trustee, by manual signature, this Certificate shall not be
entitled to any benefit under the Agreement or be valid for any purpose.


<PAGE>
                                      A-5


                  IN WITNESS WHEREOF, the Trustee has caused this Certificate to
be duly executed.


                                       SOUTHWEST AIRLINES PASS THROUGH TRUST
                                       2001-1A-2

                                       By: WILMINGTON TRUST COMPANY,
                                            as Trustee


                                       By:
                                          --------------------------------------
                                          Name:
                                          Title:



<PAGE>

               FORM OF THE TRUSTEE'S CERTIFICATE OF AUTHENTICATION


         This is one of the Certificates referred to in the within-mentioned
Agreement.


                                       WILMINGTON TRUST COMPANY,
                                            as Trustee


                                       By:
                                          --------------------------------------
                                          Name:
                                          Title:



<PAGE>

                                    EXHIBIT B


                         [DTC Letter of Representations]