Array of random values (match-ups)

Say I have four people and need to pair them off, one pair per week:

      A  B  C  D
   A  -
   B     -
   C        -
   D           -

The goal is to generate a series of random numbers such that each person is paired with each other person exactly once:

      A  B  C  D
   A  -  1  3  2
   B  1  -  2  3
   C  3  2  -  1
   D  2  3  1  -

I cannot figure out how to generate random numbers in this way. Is there any clever way you all an think of to accomplish this?

This is similar to many matched-pair schedules I have seen, but I need a way to make it randomized.