Quark mass corrections to the tau hadronic width play a significant role only for the strange quark. The complete determination of tau decays into strange hadronic final states performed by ALEPH allows the extraction of the strange spectral function. New results on strange decay modes from other experiments are also incorporated into the present analysis. Using as input moments of the spectral function the analysis leading to the determination of rn is conducted using reasonable theoretical constraints on the nonperturbative components. Careful attention is paid to the treatment of the perturbative expansions of the moments which exhibit convergence problems. The result obtained, m(s) (M-tau(2)) = (120 +/- 11(exp) +/- 8(Vus) +/- 19(th)) MeV = (120(-26)(+21)) MeV, is stable over the scale from M-tau(2) down to about 2 GeV2. Its evolution yields m(s)(1 GeV2) = (160(-35)(+28)) MeV and m(s)(4 GeV2) = (116(-26)(+20)) MeV.