  We determine the renormalization group invariant quark mass corresponding to
the sum of the strange and the average light quark mass in the quenched
approximation of QCD, using as essential input the mass of the K-mesons. In the
continuum limit we find $(M_s + M_{light})/F_K=0.874(29)$, which includes
systematic errors. Translating this non-perturbative result into the running
quark masses in the $\msbar$-scheme at $\mu=2 GeV$ and using the quark mass
ratios from chiral perturbation theory, we obtain $\mbar_s(2 GeV)=97(4) MeV$.
With the help of recent results by the CP-PACS Collaboration, we estimate that
a 10% higher value would be obtained if one replaced $F_K$ by the nucleon mass
to set the scale. This is a typical ambiguity in the quenched approximation.
