  A search for T-violating transverse muon polarization ($P_T$) in the
$K^{+}\to \pi^{0}\mu^{+}\nu$ decay was performed using kaon decays at rest. A
new improved value, $P_T= -0.0017\pm 0.0023 (stat)\pm 0.0011 (syst)$, was
obtained giving an upper limit, $| P_T | < 0.0050$. The T-violation parameter
was determined to be Im$\xi = -0.0053 \pm 0.0071(stat)\pm 0.0036(syst)$ giving
an upper limit, $|$Im$\xi| <0.016$.
