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                                                                    Exhibit 4.20

                       LIMITED LIABILITY COMPANY AGREEMENT

                                       OF

                          CAPITAL ONE CAPITAL III, LLC

     This Limited Liability Company Agreement (this "Agreement") of Capital One
Capital III, LLC is entered into by Capital One Bank, a limited purpose Virginia
state-chartered bank, as the managing member (the "Member").

     The Member, by its execution of the Certificate of Formation and this
Agreement, hereby forms a limited liability company pursuant to and in
accordance with the Delaware Limited Liability Company Act (6 Del. C.ss.18-101,
et seq.), as amended from time to time (the "Act"), and hereby agrees as
follows:

     1.   Name. The name of the limited liability company formed hereby is
          ----
Capital One Capital III, LLC (the "Company").

     2.   Certificates. Bernard J. Kelley, as an authorized person within the
          ------------
meaning of the Act, shall execute, deliver and file the Certificate of Formation
of the Company with the Secretary of State of the State of Delaware (the
"Secretary of State"). Upon the filing of the Certificate of Formation of the
Company with the Secretary of State, his powers as an authorized person shall
cease and the Member and any Officer, acting individually, shall thereafter be
designated as an authorized person within the meaning of the Act and shall
execute, deliver and file any amendments and/or restatements of the Certificate
of Formation of the Company and any other certificates required or permitted to
be filed with the Secretary of State (and any amendments and/or restatements
thereof). The Member or any Officer, acting individually, shall execute, deliver
and file any other certificates (and any amendments and/or restatements thereof)
necessary for the Company to qualify to do business in a jurisdiction in which
the Company may wish to conduct business.

     3.  Purpose. The Company is formed for the object and purpose of, and the
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nature of the business to be conducted and promoted by the Company is, engaging
in any lawful act or activity for which limited liability companies may be
formed under the Act and engaging in any and all lawful activities necessary or
incidental to the foregoing.

     4.  Powers. The business and affairs of the Company shall be managed by the
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Member. The Member shall have the power to do any and all acts necessary,
convenient or incidental to or for the furtherance of the purposes described
herein, including all powers, statutory or otherwise, possessed by members under
the laws of the State of Delaware.

     5.  Principal Business Office. The principal business office of the Company
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shall be c/o Capital One Financial Corporation, 2980 Fairview Park Drive, Suite
1300, Falls Church, Virginia, 22042-4525, or any other such location as may
hereafter be determined by the Member.

     6.  Registered Office. The address of the registered office of the Company
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in the State of Delaware is c/o The Corporation Trust Company, Corporation Trust
Center, 1209 Orange Street, Wilmington, New Castle County, Delaware, 19801.

     7.  Registered Agent. The name and address of the registered agent of the
         ----------------
Company for service of process on the Company in the State of Delaware is The
Corporation Trust Company, Corporation Trust Center, 1209 Orange Street,
Wilmington, New Castle County, Delaware, 19801.

     8.  Members. The name and the mailing address of the Member are set forth
         -------
in the records of the Company.

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     9.   Limited Liability. Except as otherwise provided by the Act, the debts,
          -----------------
obligations and liabilities of the Company, whether arising in contract, tort or
otherwise, shall be solely the debts, obligations and liabilities of the
Company, and the Member shall not be obligated personally for any such debt,
obligation or liability of the Company solely by reason of being a member of the
Company.

     10.  Admission and Capital Contribution. The Member is admitted as the
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Member of the Company upon its execution and delivery of this Agreement. The
Member will contribute $100.00 to the Company.

     11.  Additional Capital Contributions. The Member is not required to make
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any additional capital contributions to the Company. However, the Member may
make additional capital contributions to the Company at any time.

     12.  Allocation of Profits and Losses. The Company's profits and losses
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shall be allocated to the Member.

     13.  Distributions. Distributions shall be made to the Member at the times
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and in the aggregate amounts determined by the Member. Notwithstanding any
provision to the contrary contained in this Agreement, the Company shall not be
required to make a distribution to the Member on account of its interest in the
Company if such distribution would violate Section 18-607 or 18-804 of the Act
or other applicable law.

     14.  Management. In accordance with Section 18-402 of the Act, management
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of the Company shall be vested in the Member. The Member shall have the power to
do any and all acts necessary, convenient or incidental to or for the
furtherance of the purposes described herein, including all powers, statutory or
otherwise, possessed by members of a limited liability company under the laws of
the State of Delaware. Notwithstanding any other provision of this Agreement,
the Member is authorized to execute, deliver and perform any document on behalf
of the Company without any vote or consent of any other person or entity.

     15.  Officers. The Member may, from time to time as it deems advisable,
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appoint officers of the Company (the "Officers") and assign in writing titles
(including, without limitation, President, Vice President, Secretary, and
Treasurer) to any such person. Unless the Member decides otherwise, if the title
is one commonly used for officers of a business corporation formed under the
Delaware General Corporation Law, the assignment of such title shall constitute
the delegation to such person of the authorities and duties that are normally
associated with that office for such a business corporation. Any delegation
pursuant to this Section 15 may be revoked at any time by the Member.

     16.  Other Business. The Member may engage in or possess an interest in
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other business ventures (unconnected with the Company) of every kind and
description, independently or with others. The Company shall not have any rights
in or to such independent ventures or the income or profits therefrom by virtue
of this Agreement.

     17.  Exculpation and Indemnification. No Member or Officer shall be liable
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to the Company, or any other person or entity who has an interest in the
Company, for any loss, damage or claim incurred by reason of any act or omission
performed or omitted by such Member or Officer in good faith on behalf of the
Company and in a manner reasonably believed to be within the scope of the
authority conferred on such Member or Officer by this Agreement, except that a
Member or Officer shall be liable for any such loss, damage or claim incurred by
reason of such Member's or Officer's gross negligence or willful misconduct. To
the fullest extent permitted by applicable law, a Member or Officer shall be
entitled to indemnification from the Company for any loss, damage or claim
incurred by such Member or Officer by reason of any act or omission performed or
omitted by such Member or Officer in good faith on behalf of the Company and in
a manner reasonably believed to be within the scope of the authority conferred
on such Member or Officer by this Agreement, except that no Member or Officer
shall be entitled to be indemnified in respect of any loss, damage or claim
incurred by such Member or Officer by reason of gross negligence or willful
misconduct

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with respect to such acts or omissions; provided, however, that any indemnity
                                        --------  -------
under this Section 17 shall be provided out of and to the extent of Company
assets only, and the Member shall not have personal liability on account
thereof.

     18.  Assignments. The Member may assign in whole or in part its limited
          -----------
liability company interest. If a Member transfers all of its interest in the
Company pursuant to this Section 18, the transferee shall be admitted to the
Company upon its execution of an instrument signifying its agreement to be bound
by the terms and conditions of this Agreement. Such admission shall be deemed
effective immediately prior to the transfer, and, immediately following such
admission, the transferor Member shall cease to be a member of the Company.

     19.  Resignation. The Member may resign from the Company. If the Member
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resigns pursuant to this Section 19, an additional member shall be admitted to
the Company, subject to Section 20, upon its execution of an instrument
signifying its agreement to be bound by the terms and conditions of this
Agreement. Such admission shall be deemed effective immediately prior to the
resignation, and, immediately following such admission, the resigning Member
shall cease to be a member of the Company.

     20.  Admission of Additional Members. One (1) or more additional members of
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the Company may be admitted to the Company with the written consent of the
Member.

     21.  Dissolution.
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          a.  The Company shall dissolve, and its affairs shall be wound up upon
the first to occur of the following: (i) the written consent of the Member, (ii)
the retirement, resignation or dissolution of the last remaining member of the
Company or the occurrence of any other event which terminates the continued
membership of the last remaining member of the Company in the Company, unless
the business of the Company is continued in a manner permitted by the Act, or
(iii) the entry of a decree of judicial dissolution under Section 18-802 of the
Act.

          b.  The bankruptcy (as defined in Sections 18-101(1) and 18-304 of the
Act) of the Member will not cause the Member to cease to be a member of the
Company and upon the occurrence of such an event, the business of the Company
shall continue without dissolution.

          c.  In the event of dissolution, the Company shall conduct only such
activities as are necessary to wind up its affairs (including the sale of the
assets of the Company in an orderly manner), and the assets of the Company shall
be applied in the manner, and in the order of priority, set forth in Section
18-804 of the Act.

     22.  Separability of Provisions. Each provision of this Agreement shall be
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considered separable and if for any reason any provision or provisions herein
are determined to be invalid, unenforceable or illegal under any existing or
future law, such invalidity, unenforceability or illegality shall not impair the
operation of or affect those portions of this Agreement which are valid,
enforceable and legal.

     23.  Counterparts. This Agreement may be executed in any number of
          ------------
counterparts, each of which shall be deemed an original of this Agreement.

     24.  Entire Agreement. This Agreement constitutes the entire agreement of
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the Member with respect to the subject matter hereof.

     25.  Governing Law. This Agreement shall be governed by, and construed
          -------------
under, the laws of the State of Delaware (without regard to conflict of laws
principles), all rights and remedies being governed by said laws.

     26.  Amendments. This Agreement may not be modified, altered, supplemented
          ----------
or amended except pursuant to a written agreement executed and delivered by the
Member.

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     IN WITNESS WHEREOF, the undersigned, intending to be legally bound hereby,
has duly executed this Agreement as of the 23 day of January, 2002.

                                    CAPITAL ONE BANK

                                    By:  /s/ Stephen Linehan
                                         --------------------------------
                                         Name:  Stephen Linehan
                                         Title: Vice President, Corporate
                                                Treasury & Assistant Treasurer<PAGE>

                                                                    Exhibit 4.21

                            CERTIFICATE OF FORMATION

                                       OF

                           CAPITAL ONE CAPITAL IV, LLC

     This Certificate of Formation of Capital One Capital IV, LLC (the
"Company"), dated as of January __, 2002, has been duly executed and is being
filed by Bernard J. Kelley, as an authorized person, to form a limited liability
company under the Delaware Limited Liability Company Act (6 Del. C. (S)18-101,
                                                            -------
et seq.), as amended from time to time.
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     FIRST. The name of the limited liability company formed hereby is Capital
One Capital IV, LLC.

     SECOND. The address of the registered office of the Company in the State of
Delaware is c/o The Corporation Trust Company, Corporation Trust Center, 1209
Orange Street, Wilmington, New Castle County, Delaware 19801.

     THIRD. The name and address of the registered agent for service of process
on the Company in the State of Delaware are The Corporation Trust Company,
Corporation Trust Center, 1209 Orange Street, Wilmington, New Castle County,
Delaware 19801.

     IN WITNESS WHEREOF, the undersigned authorized person has executed this
Certificate of Formation as of the date first above written.

                                         /s/ Bernard J. Kelley
                                        -----------------------------
                                        Name: Bernard J. Kelley
                                        Authorized Person

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