  We extend the application of axial Ward identities to calculate $b_A, b_P$
and $b_T$, 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 $Z_P^0$ (or $Z_S^0$) and $Z_T$ are
undetermined. We present results of a pilot numerical study using hadronic
correlators.
