RHYTHMS NET CONNECTIONS INC
S-4/A, EX-3.6, 2000-06-16
TELEPHONE COMMUNICATIONS (NO RADIOTELEPHONE)
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<PAGE>

                            CERTIFICATE OF AMENDMENT
                                       OF
                      RESTATED CERTIFICATE OF INCORPORATION
                                       OF
                           RHYTHMS NETCONNECTIONS INC.

                         (Pursuant to Section 242 of the
                General Corporation Law of the State of Delaware)

     Rhythms NetConnections Inc. (the "CORPORATION"), a corporation organized
and existing under the General Corporation Laws of the State of Delaware (the
"GENERAL CORPORATION LAW"),

     DOES HEREBY CERTIFY:

     FIRST: That the Corporation was originally incorporated in Delaware under
the name Accelerated Connections, Inc., on February 27, 1997. On April 8, 1999,
the Corporation filed its Restated Certificate of Incorporation under the name
of Rhythms NetConnections Inc. (the "RESTATED CERTIFICATE"). The Restated
Certificate became effective April 12, 1999.

     SECOND: This Certificate of Amendment was duly adopted by unanimous written
consent of the members of the board of directors of the Corporation and by the
shareholders in accordance with the provisions of Sections 141 and 242 of the
General Corporation Law and it amends and restates provisions of the Restated
Certificate.

     THIRD: Article IV, Section (A), of the Restated Certificate is hereby
amended and restated in its entirety to read as follows:

          "(A) CLASSES OF STOCK. This corporation is authorized to issue two
classes of stock, denominated Common Stock and Preferred Stock. The Common Stock
shall have a par value of $0.001 per share and the Preferred Stock shall have a
par valued of $0.001 per share. The total number of shares of Common Stock which
the Corporation is authorized to issue is Two Hundred Fifty Million shares
(250,000,000), and the total number of shares of Preferred Stock which the
Corporation is authorized to issue is Ten Million shares (10,000,000), of which
one million (1,000,000) shares shall be designated Series 1 Junior Participating
Preferred Stock (the "Series 1 Preferred Stock") and the remaining shares shall
be undesignated as to series."

                [THE REMAINDER OF PAGE LEFT BLANK INTENTIONALLY]

<PAGE>

     IN WITNESS WHEREOF, this Certificate of Amendment of the Restated
Certificate has been subscribed to this 26th day of May, 2000, by the
undersigned who certifies that the statements made herein are true and correct.


                                       RHYTHMS NETCONNECTIONS INC.


                                       By: /s/ John W. Braukman
                                          --------------------------------
                                       Name (Print): John W. Braukman
                                                    ----------------------
                                       Title: Chief Financial Officer
                                             -----------------------------


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