  We search for lepton-flavor-violating tau decays into three leptons (electron
or muon) using 535 fb^{-1} of data collected with the Belle detector at the
KEKB asymmetric-energy e+e- collider. No evidence for these decays is observed
and we set 90% confidence level upper limits on the branching fractions between
2.0x10^{-8} and 4.1x10^{-8}. These results improve the best previously
published upper limits by factors from 4.9 to 7.0.
