We demonstrate how operator regularization can be used to compute radiative corrections to Green's functions involving composite operators. No divergences are encountered and no symmetry-breaking regulating parameter need be introduced into the initial Lagrangian. We demonstrate the technique to one-loop order by considering operators of dimension four in the [Formula: see text] model and the operator [Formula: see text] in an axial model. Anomalous dimensions of these operators are determined by considering finite Green's functions. There is no need to define "oversubtracted" operators to maintain linearity, as is the case when one uses BPH subtraction, nor is there an ambiguity between the trace of [Formula: see text] and [Formula: see text], as occurs in dimensional regularization. Quantities such as γ5, εμνλσ, and εμν (which are well-defined only in an integer number of dimensions) are treated unambiguously as we never alter the dimensionality of the problem.