An evaluation of the effective QED coupling at the scale M_Z is
presented. It employs the predictions of perturbative QCD for the
cross section of electron positron annihilation into hadrons up to order
\alpha_s^2, including the full quark mass dependence, and of order
\alpha_s^3 in the high energy region. This allows to predict the input
for the dispersion relations over a large part of the integration
region. The perturbative piece is combined with data for
the lower energies and the heavy quark thresholds. The result for the
hadronic contribution to the running of the coupling
\Delta\alpha^{(5)}_{\rm had}(M_Z^2)= (277.5 \pm 1.7)\times 10^{-4}
leads to (\alpha(M_Z^2))^{-1}=128.927 \pm 0.023. Compared to previous
analyses the uncertainty is thus significantly reduced.
