The mass of the tau lepton has been measured in the decay mode tau-->3pinutau using a pseudomass technique. The result obtained from 414 fb-1 of data collected with the Belle detector is Mtau=[1776.61+/-0.13(stat)+/-0.35(sys)] MeV/c2. The upper limit on the relative mass difference between positive and negative tau leptons is |Mtau+-Mtau-|/Mtau<2.8 x 10-4 at 90% confidence level.