A data-driven energy scan in the immediate vicinity of the τ pair production threshold has been performed using the Beijing Spectrometer at the Beijing Electron-Positron Collider. Approximately 5pb-1 of data, distributed over 12 scan points, have been collected. A previous mass value for the τ lepton, obtained using only the eµ final state, has been published. In this paper, the final BES result on the mass measurement is presented. The analysis is based on the combined data from the ee, eµ, eh, µµ, µh, and hh final states, where h denotes a charged Π or K. A maximum likelihood fit to the τ pair production cross section data yields the value mT=1776.96-0.21 -0.17+0.18+0.25. © 1995 The American Physical Society.