We extend the application of vector and axial Ward identities to calculate bA, bP and bT, coefficients that give the mass dependence of the renormalization constants of the corresponding bilinear operators in the quenched theory. The extension relies on using operators with non-degenerate quark masses. It allows a complete determination of the O(a) improvement coefficients for bilinears in the quenched approximation using Ward Identities alone. Only the scale dependent normalization constants Z0P (or Z0S) and ZT are undetermined. We present results of a pilot numerical study using hadronic correlators.