Update of the Search for the Neutrinoless Decay τto μγ

We present an update of the search for the lepton family number violating decay $\tau \to \mu\gamma$ using a complete CLEO II data sample of 12.6 million $\tau^+\tau^-$ pairs. No evidence of a signal has been found and the corresponding upper limit is $ \BR(\tau \to \mu\gamma) < 1.0 \times 10^{-6} $ at 90% CL, significantly smaller than previous limits. All quoted results are preliminary.