  We study the evolution of the gauge coupling and the anomalous dimension of
the mass towards an infrared fixed point for non-supersymmetric gauge theories
in the modified regularization invariant, RI', scheme. This is done at the
three loop level where all the renormalization group functions have been
calculated explicitly. The purpose is to assess the scheme dependence of
earlier and similar investigations performed at three and four loop order in
the modified minimal subtraction, $\bar{\text{MS}}$, scheme. Our results are of
the same order when compared to the $\bar{\text{MS}}$ scheme.
