  The MEG experiment makes use of one of the world's most intense low energy
muon beams, in order to search for the lepton flavour violating process
$\mu^{+} \rightarrow {\rm e}^{+} \gamma$. We determined the residual beam
polarization at the thin stopping target, by measuring the asymmetry of the
angular distribution of Michel decay positrons as a function of energy. The
initial muon beam polarization at the production is predicted to be $P_{\mu} =
-1$ by the Standard Model (SM) with massless neutrinos. We estimated our
residual muon polarization to be $P_{\mu} = -0.85 \pm 0.03 ~ {\rm (stat)} ~ {
}^{+ 0.04}_{-0.05} ~ {\rm (syst)}$ at the stopping target, which is consistent
with the SM predictions when the depolarizing effects occurring during the muon
production, propagation and moderation in the target are taken into account.
The knowledge of beam polarization is of fundamental importance in order to
model the background of our ${\megsign}$ search induced by the muon radiative
decay: $\mu^{+} \rightarrow {\rm e}^{+} \bar{\nu}_{\mu} \nu_{\rm e} \gamma$.
