  We present two determinations of the coefficient $c_A$ in quenched QCD,
needed to build the $O(a)$ improved axial current. The first condition used is
the requirement that the PCAC quark mass, as a function of $x_0$, stays flat
for a non-trivial spatial phase for the fermions in the Schr\"odinger
functional. The second condition is that the PCAC relation for the ground-state
and the first excited state at finite L give the same quark mass. Our results
confirm previous findings that in the quenched theory the intrinsic $O(a)$
ambiguity of $c_A$ gets relevant around $\beta\simeq6.0$.
