We present the result from a precision measurement of the mass of the $\tau$ lepton, $M_\tau$, based on $423 fb^{-1}$ of data recorded at the $\Upsilon(4S)$ resonance with the BaBar detector. Using a pseudomass endpoint method, we determine the mass to be $1776.68 \pm 0.12 (stat) \pm 0.41 (syst) MeV$. We also measure the mass difference between the $\tau^+$ and $\tau^-$, and obtain $(M_{\tau^{+}}-M_{\tau^{-}})/M^\tau_{AVG} = (-3.4 \pm 1.3 (stat) \pm 0.3 (syst)) \times 10^{-4}$, where $M^\tau_{AVG}$ is the average value of $M_{\tau^+}$ and $M_{\tau^-}$.

Comment: 15 pages, 10 figures, submitted to Phys. Rev. D