Exhibit 4.01
      THIRD SUPPLEMENTAL INDENTURE, dated as of February 20, 2001 (the "Third
Supplemental Indenture"), to the Indenture, dated as of April 15, 1996 (the
"Indenture") between ADELPHIA BUSINESS SOLUTIONS, INC. (formerly known as
Hyperion Telecommunications, Inc.), a Delaware corporation (the "Company"), and
THE BANK OF NEW YORK (successor trustee by acquisition to Harris Trust Company
of New York, formerly known as Bank of Montreal Trust Company), a trust company
organized under the laws of the State of New York (the "Trustee").

      WHEREAS, the Company has duly authorized the execution and delivery of the
Indenture to provide for the issuance of 13% Senior Discount Notes due 2003,
Series A and Series B (the "Notes"); and

      WHEREAS, the Company desires and has requested the Trustee to join it in
the execution and delivery of this Third Supplemental Indenture in order to cure
an ambiguity and make a change that does not adversely affect the legal rights
under the Indenture of any Holder of the Notes;

      WHEREAS, Section 9.01 of the Indenture provides that a supplemental
indenture may be entered into by the Company and the Trustee to cure an
ambiguity in the Indenture or to make a change that does not adversely affect
the legal rights under the Indenture of any Holder of the Notes without the
consent of any holder of any Note provided certain conditions are met; and

      WHEREAS, the conditions set forth in the Indenture for the execution and
delivery of this Third Supplemental Indenture have been complied with; and

      WHEREAS, all things necessary to make this Third Supplemental Indenture a
valid agreement of the Company and the Trustee, in accordance with its terms,
and a valid amendment of, and supplement to, the Indenture, have been done;

      NOW THEREFORE, in consideration of the premises and the mutual covenants
herein, the Company agrees with the Trustee that the Indenture is supplemented
and amended, solely to the extent and for the purposes expressed herein, as
follows:

      Section 1.  Definitions.  Any capitalized term used herein and not
otherwise defined herein shall have the meaning given in the Indenture.

      Section 2. Amendments to Section 4.07. Clause (y)(2)(C) of the first
paragraph of Section 4.07, Restricted Payments, is amended by inserting after
the word "convertible" the phrase "or converted" and by inserting the phrase "or
exchanged for" following each use of the word "into" in clause (y)(2)(C)
resulting in clause (y)(2)(C) reading in its entirety as follows:

      "(C) from the issuance and sale of Indebtedness that is convertible or
      converted into or exchanged for Common Stock (other than Disqualified
      Stock), to the extent such Indebtedness is actually converted into or
      exchanged for such Common Stock (clauses (A), (B) and (C) collectively

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      referred to as "Equity Issuances"), other than any such net cash proceeds
      from Equity Issuances that were used as set forth in clause (c) and (d)
      below; and"

      The second paragraph of Section 4.07, Restricted Payments, which follows
clause (z) of the first paragraph is amended by the addition of a new clause (g)
which reads in its entirety as follows:

      "(g) the redemption, repurchase, retirement, defeasance or other
acquisition of any subordinated Indebtedness of the Company or of any Equity
Interests of the Company (1) upon the conversion thereof into or the exchange
thereof for Equity Issuances (other than Disqualified Stock) of the Company, or
(2) out of the net cash proceeds of the substantially concurrent sale (other
than to a Subsidiary of the Company) of Equity Issuances of the Company (other
than Disqualified Stock), provided that in the case of subclause (2) the amount
of any such net cash proceeds that are utilized for any such redemption,
repurchase, retirement, defeasance or other acquisition shall be excluded from
clause (c) (2) and (d) above and clause (y) of the preceding paragraph."


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      IN WITNESS WHEREOF, the parties hereto have caused this Third Supplemental
Indenture to be duly executed, and attested, all as of the date and first year
above written.

ATTEST:                             ADELPHIA BUSINESS SOLUTIONS, INC.



/s/ John Glicksman                  By: /s/ James P. Rigas
Its Assistant Secretary             Its Chief Executive Officer



ATTEST:                             THE BANK OF NEW YORK,
                                          successor trustee by acquisition to
                                          Harris Trust Company of New York,
                                          formerly known as Bank of Montreal
                                          Trust Company, as Trustee

_____________________________       By: /s/ Terence Rawlins
Assistant Secretary                         Assistant Vice President