  A finite-size technique is employed to compute the normalization constant
$Z_A$ of the isovector axial current in lattice QCD. The calculation is carried
out in the quenched approximation for values of the bare gauge coupling $g_0$
ranging from 0 to 1. In the lattice action and the lattice expression for the
axial current we include the counterterms required for O(a) improvement, with
non-perturbatively determined coefficients. With little additional work the
normalization constant $Z_V$ of the improved isospin current is also obtained.
