We critically examine the evaluation of the hadronic contribution to t
he running of the QED coupling, alpha, from Q(2) = 0 to Q(2) = M(Z)(2)
. Using data for e(+)e(-) --> hadrons we find that alpha(M(Z)(2))(-1)
= 128.99+/-0.06, as compared to the existing value of 128.87+/-0.12.