  The perturbative quark mass corrections to the tau hadronic width are studied
to O(alpha_s^3 m_q^2). Including up to dimension four corrections, we get m_s(4
GeV^2)=(143 \pm 42) MeV [m_s(1 GeV^2)=(193 \pm 59) MeV ]. Possible improvements
to reduce the theoretical uncertainty are pointed out.
