<PAGE>
                                                                   EXHIBIT 10r-4

                                SECOND AMENDMENT
                                     TO THE
                              BELLSOUTH CORPORATION
                      TRUST UNDER EXECUTIVE BENEFIT PLAN(S)

         THIS SECOND AMENDMENT to the BellSouth Corporation Trust Under
Executive Benefit Plan(s) (the "Trust Agreement") is made this 17th day of
December, 2003, by and between BellSouth Corporation, a Georgia
corporation ("Company"), and The Northern Trust Company, an Illinois corporation
of Chicago, Illinois ("Trustee"):

         WHEREAS, Company and Bankers Trust Company, a New York Corporation
("Bankers Trust"), first executed the Trust Agreement on May 23, 1996; and

         WHEREAS, Company on November 1, 2003, appointed Trustee as successor
trustee to Bankers Trust Company; and

         WHEREAS, Company and Trustee, effective November 1, 2003, executed a
First Amendment to the Trust Agreement; and

         WHEREAS, Company and Trustee now desire to amend further the Trust
Agreement, pursuant to Section 12 of the Trust Agreement;

         NOW, THEREFORE, the sections of the Trust Agreement set forth below are
amended as follows, but all other sections of the Trust Agreement shall remain
in full force and effect:

                                       1.

         Section 5(c) is hereby amended by deleting the last sentence therein,
and inserting at the end of Section 5(c) the following:

                  "Furthermore, in addition to such reservation of discretionary
                  authority, prior to a Change of Control, Company may appoint
                  one or more investment managers ("Investment Managers") to
                  manage all or a portion of the assets of the Trust. Company
                  shall notify Trustee of each appointment of an Investment
                  Manager (and of any subsequent changes in any such
                  appointment), in writing, and shall direct each Investment
                  Manager to certify to Trustee the names of all persons
                  authorized to act on its behalf. Trustee may continue to rely
                  upon such instruments until otherwise notified in writing by
                  Company or the Investment Manager, as the case may be. Trustee
                  may conclusively rely upon the determinations of and
                  directions



<PAGE>

                  from Company acting pursuant to the authority reserved in, or
                  an Investment Manager appointed pursuant to, subsection (c) of
                  this Section 5. All fees and expenses of an Investment Manager
                  shall be paid from the assets of the Trust unless paid by
                  Company. Notwithstanding anything to the contrary contained
                  herein, following a Change of Control, Company may not reserve
                  discretionary authority or appoint an Investment Manager for
                  the management and control of any assets of the Trust and any
                  prior reservation or appointment then in effect shall be
                  nullified."

                                       2.

         Section 5(d) is hereby deleted in its entirety and replaced with the
following:

                  "(d) Trustee shall follow the directions of Company or of an
                  Investment Manager regarding the investment and reinvestment
                  of Trust assets (or such portion thereof as may be under
                  management by Company or an Investment Manager pursuant to
                  subsection (c) of this Section 5), and shall be under no duty
                  or obligation to review or to question any direction of
                  Company pursuant to the authority reserved in, or of an
                  Investment Manager appointed pursuant to, subsection (c) of
                  this Section 5, or to review any investment to be acquired,
                  held or disposed of pursuant to such directions, or to make
                  recommendations with respect to the disposition or continued
                  retention of any such investment and Trustee shall have no
                  authority to take any action or to refrain from taking any
                  action with respect to any such assets unless and until it is
                  directed to do so by Company pursuant to authority reserved
                  in, or an Investment Manager appointed pursuant to, subsection
                  (c) of this Section 5. Notwithstanding anything to the
                  contrary in this Trust Agreement, Company shall indemnify
                  Trustee and hold it harmless from any liability or expense
                  (including reasonable attorneys' fees) resulting from acts or
                  omissions of Trustee taken in reliance on directions or the
                  absence of directions from Company pursuant to authority
                  reserved in, or an Investment Manager appointed pursuant to,
                  subsection (c) of this Section 5 or otherwise in connection
                  with Trustee's administration of the Trust consistent with
                  subsection (c) of Section 5."


                                       2

<PAGE>


                                       3.

         Section 5(e) is hereby amended by substituting "Company pursuant to
authority reserved in subsection (c) of this Section 5" with "Company pursuant
to authority reserved in, or an Investment Manager appointed pursuant to,
subsection (c) of this Section 5" therein.

                                       4.

         Section 5(f) is hereby amended by substituting "Company acting pursuant
to authority reserved under subsection (c) of this Section 5" with "Company
acting pursuant to authority reserved in, or an Investment Manager appointed
pursuant to, subsection (c) of this Section 5" in the introductory language
preceding clause (1) of Section 5(f).

                                       5.

         Section 5(g) is hereby amended by adding at the end thereof the
following:

         "Notwithstanding the foregoing, the Trustee shall vote any proxies for
         such shares of Company Stock held pursuant to this Section 5(g) in its
         discretion."

         IN WITNESS WHEREOF, Company and Trustee have caused this Amendment to
be executed and their respective corporate seals to be affixed and attested by
their corporate officers on the day and year first written above.

                                 BELLSOUTH CORPORATION



                              By: /s/ Lynn Wentworth
                                 --------------------------------------------
                              Its: Chairman, Trust Asset Management Committee


ATTEST:



/s/ Marcy A. Bass
Its: Senior Corporate Counsel & Asst. Corporate Secretary


         (CORPORATE SEAL)


                                      3


<PAGE>

         The undersigned, Marcy A, Bass, does hereby certify that he/she is the
duly elected, qualified and acting Assistant Corporate Secretary of BellSouth
Corporation ("Company") and further certifies that the person whose signature
appears above is a duly elected, qualified and acting officer of Company with
full power and authority to execute this Trust Amendment on behalf of Company
and to take such other actions and execute such other documents as may be
necessary to effectuate this Trust Amendment.


/s/ Marcy A. Bass
Senior Corporate Counsel and
Assistant Corporate Secretary
BellSouth Corporation





                                THE NORTHERN TRUST COMPANY


                                By: /s/ Anita L. Bender
                                Its: Vice President



ATTEST:

/s/ Robert F. Draths

Its:  Assistant Secretary


                                       4