  Quark mass corrections to the tau hadronic width play a significant role only
for the strange quark, hence providing a method for determining its mass. The
experimental input is the vector plus axial-vector strange spectral function
derived from a complete study of tau decays into strange hadronic final states
performed by ALEPH. New results on strange decay modes from other experiments
are also incorporated. The present analysis determines the strange quark mass
at the Mtau mass scale using moments of the spectral function. Justified
theoretical constraints are applied to the nonperturbative components and
careful attention is paid to the treatment of the perturbative expansions of
the moments which exhibit convergence problems. The result obtained,
m_s(Mtau^2) = (120 +- 11_exp +- 8_Vus +- 19_th) MeV = (120^+21_-26) MeV, is
stable over the scale from Mtau down to about 1.4 GeV. Evolving this result to
customary scales yields m_s(1 GeV^2) = (160^+28_-35) MeV and m_s(4 GeV^2) =
(116^+20_-25) MeV.
