  We extend the application of vector and 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.
