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 $τ\to μγ$ using a complete CLEO II data sample of 12.6 million $τ^+τ^-$ pairs. No evidence of a signal has been found and the corresponding upper limit is $ \BR(τ\to μγ) < 1.0 \times 10^{-6} $ at 90% CL, significantly smaller than previous limits. All quoted results are preliminary.

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