  We compute the relation between the quark mass defined in the minimal
modified $\MSbar$ scheme and the mass defined in the ``Regularization
Invariant" scheme (RI), up to the NNLO order. The RI scheme is conveniently
adopted in lattice QCD calculations of the quark mass, since the relevant
renormalization constants in this scheme can be evaluated in a non-perturbative
way. The NNLO contribution to the conversion factor between the quark mass in
the two schemes is found to be large, typically of the same order of the NLO
correction at a scale $\mu \sim 2$ GeV. We also give the NNLO relation between
the quark mass in the RI scheme and the renormalization group-invariant mass.
