  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.
