We have searched for neutrinoless τ lepton decays into three charged leptons using an 87.1fb-1 data sample collected with the Belle detector at the KEKB e+e- collider. Since the number of signal candidate events is compatible with that expected from the background, we set 90% confidence level upper limits on the branching fractions in the range (1.9-3.5)×10-7 for various decay modes τ -→ℓ-ℓ+ℓ- where ℓ represents e or μ. © 2004 Published by Elsevier B.V.