Limit on the tau neutrino mass from ${\tau }^{-}\to {\pi }^{-}{\pi }^{+}{\pi }^{-}{\pi }^0{\nu }_{\tau }$

From a data sample of 29058 ${\tau }^{\pm }\to {\pi }^{\pm }{\pi }^{+}{\pi }^{-}{\pi }^0{\nu }_{\tau }$ decays observed in the CLEO detector we derive a 95% confidence upper limit on the tau neutrino mass of 28 MeV.