EXHIBIT 1.1


                              INVESCO UNIT TRUSTS,
                           TAXABLE INCOME SERIES 586
                                TRUST AGREEMENT

                            Dated: November 23, 2016

   This Trust Agreement among Invesco Capital Markets, Inc., as Depositor, The
Bank of New York Mellon, as Trustee, ICE Securities Evaluations, Inc., as
Evaluator, and Invesco Investment Advisers LLC, as Supervisor, sets forth
certain provisions in full and incorporates other provisions by reference to the
document entitled "Standard Terms and Conditions of Trust For Invesco Unit
Trusts, Taxable Income Series, Effective for Unit Investment Trusts Established
On and After December 10, 2012 (Including Invesco Unit Trusts, Taxable Income
Series 429 and Subsequent Series)" (the "Standard Terms and Conditions of
Trust") and such provisions as are set forth in full and such provisions as are
incorporated by reference constitute a single instrument. All references herein
to Articles and Sections are to Articles and Sections of the Standard Terms and
Conditions of Trust.

                                WITNESSETH THAT:

   In consideration of the premises and of the mutual agreements herein
contained, the Depositor, Trustee, Evaluator and Supervisor agree as follows:

                                     PART I

                     STANDARD TERMS AND CONDITIONS OF TRUST

   Subject to the provisions of Part II hereof, all the provisions contained in
the Standard Terms and Conditions of Trust are herein incorporated by reference
in their entirety and shall be deemed to be a part of this instrument as fully
and to the same extent as though said provisions had been set forth in full in
this instrument.

                                    PART II

                     SPECIAL TERMS AND CONDITIONS OF TRUST

   The following special terms and conditions are hereby agreed to:

   1. The Bonds listed in the Schedule hereto have been deposited in trust under
this Trust Agreement.

   2. The fractional undivided interest in and ownership of the Trust
represented by each Unit thereof is a fractional amount, the numerator of which
is one and the denominator of which is the amount set forth under "Summary of
Essential Financial Information--General Information--Number of Units" in the
Prospectus for the Trust.

   3. The term "First Settlement Date" shall mean the date set forth in footnote
3 under "Summary of Essential Financial Information" in the Prospectus for the
Trust.

   4. The term "Monthly Distribution Date" shall mean the "Distribution Dates"
set forth under "Summary of Essential Financial Information--Estimated
Distributions" in the Prospectus for the Trust.

   5. The term "Monthly Record Date" shall mean the "Record Dates" set forth
under "Summary of Essential Financial Information--Estimated Distributions" in
the Prospectus for the Trust.

   6. All references in the Standard Terms and Conditions of Trust to "Standard
& Poor's Securities Evaluations, Inc." are hereby changed to "ICE Securities
Evaluations, Inc."

   7. All references in Section 3.05(f) of the Standard Terms and Conditions of
Trust to distributions by mail are hereby deleted.

   8. The Depositor's annual compensation rate described in Section 3.15 and the
Supervisor's annual compensation rate described in Section 4.01 collectively
shall be that amount set forth under the section entitled "Summary of Essential
Financial Information--Expenses--Supervisory, bookkeeping and administrative
service fee" in the Prospectus for the Trust.

   9. The Trustee's annual compensation as set forth under Section 7.04 shall be
that amount set forth under the section entitled "Summary of Essential Financial
Information--Expenses--Trustee's Fee" in the Prospectus for the Trust.

   IN WITNESS WHEREOF, the undersigned have caused this Trust Agreement to be
executed; all as of the day, month and year first above written.


                         INVESCO CAPITAL MARKETS, INC.

                            By: /s/ JOHN F. TIERNEY
                            -----------------------
                                 Vice President


                        INVESCO INVESTMENT ADVISERS LLC

                            By: /s/ JOHN F. TIERNEY
                            -----------------------
                     Vice President and Executive Director


                        ICE SECURITIES EVALUATIONS, INC.

                           By: /s/ FRANK A. CICCOTTO
                           -------------------------
                President & Global Head, Securities Evaluations


                          THE BANK OF NEW YORK MELLON

                           By: /s/ JOANNA YEDREYESKI
                           -------------------------
                                 Vice President



                         SCHEDULE A TO TRUST AGREEMENT

                         SECURITIES INITIALLY DEPOSITED
                                       IN
                 INVESCO UNIT TRUSTS, TAXABLE INCOME SERIES 586

      [Incorporated herein by this reference and made a part hereof is the
      "Portfolio" schedule as set forth in the Prospectus for the Trust.]