SQL question: Highest column value of unique column pairs

Hi,

I have the following table which holds the result of 1 on 1 matches:

FName1, LName1, Score1, FName2, LName2, Score2, Date
John, Doe, 85 Bill, Gates, 20 Jan 1.
John, Archer, 90 John, Doe, 120 Jan 5
Bob, Barker, 70 Calvin, Klien 8 Jan 8
John, Doe, 60 Bill, Gates, 25 Jan 3.

So columns 1 and 2 hold the first person. Column 3 holds his score.
Columns 4 and 5 hold the second person. Column 6 holds his score.

I want to return the most recent score for each person (be they an
opponent or myself). And the resultant table shouldn't care if they
are person 1 or 2.

So the end result would be

FName, LName, Score, Date
John, Doe, 120 Jan 5.
John, Archer 90 Jan 5.
Bob, Barker 70 Jan 8
Bill, Gates 25 Jan 3
Calvin Klien 8 Jan 8

Thanks for any help!