  The running of renormalized quark masses is computed in lattice QCD with two
flavors of massless O(a) improved Wilson quarks. The regularization and flavor
independent factor that relates running quark masses to the renormalization
group invariant ones is evaluated in the Schroedinger Functional scheme. Using
existing data for the scale r_0 and the pseudoscalar meson masses, we define a
reference quark mass in QCD with two degenerate quark flavors. We then compute
the renormalization group invariant reference quark mass at three different
lattice spacings. Our estimate for the continuum value is converted to the
strange quark mass with the help of chiral perturbation theory.
