  We have searched for the lepton flavor violating decays $\tau^-\to \ell^-\ks$
($\ell = e {or} \mu$), using a data sample of 281 fb$^{-1}$ collected with the
Belle detector at the KEKB $e^+e^-$ asymmetric-energy collider. No evidence for
a signal was found in either of the decay modes, and we set the following upper
limits for the branching fractions: ${\cal{B}}(\tau^-\to e^-\ks) < 5.6\times
10^{-8}$ and ${\cal{B}}(\tau^-\to \mu^-\ks) < 4.9\times 10^{-8}$ at the 90%
confidence level. These results improve the previously published limits set by
the CLEO collaboration by factors of 16 and 19, respectively.
