Using recent CLEO III results for the cross section for $e^+e^- \to
{\rm
hadrons}$ at seven center-of-mass energies between 6.964 and
10.538~GeV, we
derive a value for the
strong coupling constant
$\alpha_s(M_Z^2)=0.110_{-0.012}^{-0.010}{}_{-0.011}^{+0.010}$
where the uncertainties are uncorrelated and correlated,
respectively. Our result differs by more than one standard
deviation from the one derived by CLEO III, as a consequence of
inclusion of
quark mass effects and the proper matching between the effective
theories with
four and five flavours, respectively.