Update of the Search for the Neutrinoless Decay τ to μγ

We present an update of the search for the lepton family number violating decay tau -> mu gamma using 12.6 million tau+tau- pairs collected with the CLEO detector. No evidence of a signal has been found and the corresponding upper limit is BR(tau -> mu gamma) < 1.1x10^{-6} at 90% CL, significantly smaller than previous experimental limits.