We have searched for τ lepton decays, τ-→Λ̄π- and τ-→Λπ-, that simultaneously violate the conservation of the lepton (L) and baryon (B) number using a data sample of 154 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: B(τ-→Λ̄π-) <1.4×10-7 and B(τ-→Λπ-)<0.72×10-7 at the 90% confidence level. This is the first search ever performed for these modes. © 2005 Elsevier B.V. All rights reserved.