  The coefficients multiplying the counterterms required for O($a$) improvement
of the action and the isovector axial current in lattice QCD are computed
non-perturbatively, in the quenched approximation and for bare gauge couplings
$g_0$ in the range $0 \leq g_0 \leq 1$. A finite-size method based on the
Schr\"odinger functional is employed, which enables us to perform all
calculations at zero or nearly zero quark mass. As a by-product the critical
hopping parameter $\kappa_c$ is obtained at all couplings considered.
