  In this paper transverse positron polarization in the $\mu^+ \to e^+ \bar
{\nu_{\mu}} \nu_e$ decay in the framework of SM is considered. It is shown that
the final state interaction effect leads to nonzero transverse polarization.
Numerical value of the considered effect proved to be negligible. Thus SM
contribution to the transverse positron polarization in the $\mu^+ \to e^+ \bar
{\nu_{\mu}} \nu_e$ decay will not be the obstacle to a new physics searches.
