Swappng Filds

Hello-
I have a table with values in two columns that I want to swap; that is,
I want the value in column A to now be in column B and the value in
column B to be in column A.  I tried...

UPDATE my_table SET A=B, B=A WHERE mycontition = True

But that seemed to place the value of column B into A, then the new
value of A into B, so both A and B contained value B.  Is there a common
technique to accomplish this?

Thanks,
--greg