We report the results of a search for the decay K(L) --> pi0mu+mu- con
ducted by E799 at Fermilab. This decay mode is expected to have signif
icant CP-violating contributions and a direct measurement could either
confirm the standard model mechanisms for CP violation or point to ph
ysics beyond the standard model. No such events were seen. The 90% con
fidence level upper limit is determined to be B(K(L) --> pi0mu+mu-) <
5.1 x 10(-9).