We report results of the first measurements of Lambda and <(<Lambda>)over b
ar> polarization produced in deep inelastic polarized muon scattering on th
e nucleon. The results are consistent with an expected trend towards positi
ve polarization with increasing x(F). The polarizations of Lambda and <(<La
mbda>)over tilde> appear to have opposite signs. A large negative polarizat
ion for Lambda at low positive x(F) is observed and is not explained by exi
sting models. A possible interpretation is presented.