  The renormalisation group running of the quark mass is determined
non-perturbatively for a large range of scales, by computing the step scaling
function in the Schroedinger Functional formalism of quenched lattice QCD both
with and without O(a) improvement. A one-loop perturbative calculation of the
discretisation effects has been carried out for both the Wilson and the
Clover-improved actions and for a large number of lattice resolutions. The
non-perturbative computation yields continuum results which are regularisation
independent, thus providing convincing evidence for the uniqueness of the
continuum limit. As a byproduct, the ratio of the renormalisation group
invariant quark mass to the quark mass, renormalised at a hadronic scale, is
obtained with very high accuracy.
