A regularization-independent method is introduced to study renormalizable field theories non-perturbatively using its Schwinger-Dyson equations. The method is described in the context of QCD, and we show how the non-perturbative 2-point Green's functions can be written entirely in terms of renormalized quantities, which renders the equations manifestly finite in a regularization-independent manner. As an illustration of the technique, we apply it to a study of the fermion propagator in quenched QED₄ with the Curtis-Pennington 3-point vertex. ; Ayse Kizilersü, Andreas W. Schreiber, Tom Sizer and Anthony G. Williams