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We have searched for the decay of the τ lepton into seven charged particles and zero or one π0. The data used in the search were collected with the CLEO II detector at the Cornell Electron Storage Ring (CESR) and correspond to an integrated luminosity of 4.61 fb-. No evidence for a signal is found. Assuming all the charged particles are pions, we set an upper limit on the branching fraction B(τ-→4π-3π+(π0) ντ) < 2.4X10-6 at the 90% confidence level. This limit represents a significant improvement over the previous limit.