Non-perturbative determination of Z_A^(stat) in quenched QCD

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.