  A search for the lepton-flavor violating $\mu^{+}\rightarrow e^{+}\gamma$
decay using polarized muons is revisited in terms of suppression of the serious
background arising from an accidental coincidence between a $e^{+}$ in the
normal muon decay and a high energy photon in the radiative muon decay,
$\mu^{+} \rightarrow e^{+} \nu \overline{\nu} \gamma$. It is found that a high
energy photon in $\mu^{+} \rightarrow e^{+} \nu \overline{\nu} \gamma$ decay is
preferentially emitted parallel to the muon spin direction, similarly to
$e^{+}$ in the normal muon decay. The selective measurements of either $e^{+}$s
or photons moving antiparallel to the muon spin direction would suppress the
accidental background for $\mu^{+} \rightarrow e^{+} \gamma$ with right-handed
and left-handed $e^{+}$s respectively.
