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!