Update of the electromagnetic effective coupling constant $\alpha (M_Z^2)$

We recalculate the hadronic contribution to the effective electromagnetic coupling constant $\alpha (M_Z^2)$ using quasi-analytical approximations for the cross-section of $e^{+}{e}^{-}\to hadrons$ proposed earlier by one of the authors(N.V.K.,Mod.Phys.Lett.A9(1994)2825). We find that $\alpha^{-1}(M^2_Z) = 128.98 \pm 0.06$.