You can get the facts here, Brown:
Standing Rules of the Senate
Byrd employed Senate Rule XX, "Questions of Order":
1. A question of order may be raised at any stage of the proceedings, except when the Senate is voting or ascertaining the presence of a quorum, and, unless submitted to the Senate, shall be decided by the Presiding Officer without debate, subject to an appeal to the Senate. When an appeal is taken, any subsequent question of order which may arise before the decision of such appeal shall be decided by the Presiding Officer without debate; and every appeal therefrom shall be decided at once, and without debate; and any appeal may be laid on the table without prejudice to the pending proposition, and thereupon shall be held as affirming the decision of the Presiding Officer.
2. The Presiding Officer may submit any question of order for the decision of the Senate.
Senate Rule V provides for "Suspension and Amendment of the Rules":
1. No motion to suspend, modify, or amend any rule, or any part thereof, shall be in order, except on one day's notice in writing, specifying precisely the rule or part proposed to be suspended, modified, or amended, and the purpose thereof. Any rule may be suspended without notice by the unanimous consent of the Senate, except as otherwise provided by the rules.
2. The rules of the Senate shall continue from one Congress to the next Congress unless they are changed as provided in these rules.
Wikipedia is a wonderful resource, but i consider it less conclusive than the Senate's web site page on the Rules of the Senate.
You have misconstrued (or misunderstood) what it was that Frist intended. He was contemplating the removal of matters on the Executive Calendar (measures sent to the Senate from the White House) from the authority of Rule XXII--which would not have ended filibusters, but would only have ended filibustering treaties and Presidential appointments.
Ironically, Senator Byrd first used the point of order option in 1975 to reduce the cloture requirement from two-thirds to three-fifths.
Senate Rule XXII, Second Section, paragraphs one and two hold:
2. Notwithstanding the provisions of rule II or rule IV or any other rule of the Senate, at any time a motion signed by sixteen Senators, to bring to a close the debate upon any measure, motion, other matter pending before the Senate, or the unfinished business, is presented to the Senate, the Presiding Officer, or clerk at the direction of the Presiding Officer, shall at once state the motion to the Senate, and one hour after the Senate meets on the following calendar day but one, he shall lay the motion before the Senate and direct that the clerk call the roll, and upon the ascertainment that a quorum is present, the Presiding Officer shall, without debate, submit to the Senate by a yea-and-nay vote the question:
"Is it the sense of the Senate that the debate shall be brought to a close?" And if that question shall be decided in the affirmative by three-fifths of the Senators duly chosen and sworn -- except on a measure or motion to amend the Senate rules, in which case the necessary affirmative vote shall be two-thirds of the Senators present and voting -- then said measure, motion, or other matter pending before the Senate, or the unfinished business, shall be the unfinished business to the exclusion of all other business until disposed of.
It takes three-fifths of the quorum to end debate, and it takes two-thirds of the quorum to change Senate Rules.