Search for the Lepton-Flavor-Violating Decay<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>τ</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mo>→</mml:mo><mml:msup><mml:mi>μ</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mi>η</mml:mi></mml:math>at Belle

We have searched for the lepton flavor violating decay tau(-)-->micro(-)eta using a data sample of 84.3 fb(-1) accumulated with the Belle detector at KEK. The eta meson was detected through the decay modes: eta-->gammagamma and pi(+)pi(-)pi(0). No signal candidates are found, and we obtain an upper limit for the branching fraction B(tau(-)-->micro(-)eta)<3.4 x 10(-7) at the 90% confidence level.