  We compute non-perturbative renormalization constants of fermionic bilinears
for the chirally improved lattice fermions in the quenched approximation of
QCD. We address finite size effects and the influence of Gribov copies. Our
results are presented in the RI' and MSbar schemes as well as in RGI form and
we discuss relations between the renormalization constants implied by chiral
symmetry. After publication we corrected the numerator of the first coefficient
of \alpha_s^3 in (24) from 3696847 to 3890527, which yields a 0.2% higher value
of the conversion coefficient at \mu=2 GeV.
