Update of the search for the neutrinoless decay<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mover><mml:mrow><mml:mi>τ</mml:mi></mml:mrow><mml:mrow><mml:mo>→</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:mrow><mml:mi>μ</mml:mi><mml:mi>γ</mml:mi></mml:math>

We present an update of the search for the lepton family number violating decay $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\tau}}\ensuremath{\mu}\ensuremath{\gamma}$ using 12.6 million ${\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}}$ pairs collected with the CLEO detector. No evidence of a signal has been found and the corresponding upper limit is $\mathcal{B}(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\tau}}\ensuremath{\mu}\ensuremath{\gamma})&lt;1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ at 90% C.L., significantly smaller than previous experimental limits.