We studied the radiative muon decay $mu^+ to e^+ ubar{ u}gamma$ by using for the first time an almost fully polarized muon source. We identified a large sample (~13000) of these decays in a total sample of 1.8x10^14 positive muon decays collected in
the MEG experiment in the years 2009--2010 and measured the branching ratio B($mu^+ to e^+ ubar{ u}gamma$) = (6.03+-0.14(stat.)+-0.53(sys.))x10^-8 for E_e > 45 MeV and E_{gamma} > 40 MeV, consistent with the Standard Model prediction. The precise measurement of this decay mode provides a basic tool for the timing calibration, a normalization channel, and a strong quality check of the complete MEG experiment in the search for $mu^+ to e^+gamma$ process.
