Update of the search for the neutrinoless decay $\overrightarrow{\tau }\mu \gamma$

We present an update of the search for the lepton family number violating decay $\overrightarrow{\tau }\mu \gamma$ 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 $\mathcal{B}\left(\overrightarrow{\tau }\mu \gamma \right)<\mathrm{}1.1\mathrm{}\times {10}^{-6}$ at 90% C.L., significantly smaller than previous experimental limits.