  We non-perturbatively calculate the renormalization factor of the static
axial vector current in O(a) improved quenched lattice QCD. Its scale
dependence is mapped out in the Schroedinger functional scheme by means of a
recursive finite-size scaling technique, taking the continuum limit in each
step. We also obtain Z_A^{stat} for Wilson fermions in order to renormalize
existing unimproved data on F_B^{bare} non-perturbatively.
