  We present the preliminary results from the search of the non-conservation of
lepton flavor number in the decay of a $\tau$ to a lighter mass lepton and a
pseudo-scalar meson, performed using $e^+e^- \to \tau^+\tau^-$ events collected
at a center-of-mass energy near 10.58 GeV with the BABAR detector at the SLAC
PEP-II $e^+e^-$ storage ring. No evidence of such a signal has been found in
the data sample corresponding to a luminosity of 314.5 fb$^{-1}$, and we set an
upper limit of $1.6\times 10^{-7}$ at 90% confidence level on the decay of
$\tau^- \to \mu^-\eta$.
