  The strong coupling constant $\alpha_s(\mu)$ is extracted from the fits to
charmonium spectrum and fine structure splittings. The relativistic kinematics
is taken into account and relativistic corrections are shown to increase the
matrix elements defining spin effects up to 40%. The value of $\alpha_s(\mu)$
at low-energy scale $\mu=1.0 \pm 0.2 GeV$ was found to be $\alpha_s(\mu) = 0.38
\pm 0.03 (exp.) + 0.04 (theor.)$ which is about 50% lower than standard
perturbative two-loop approximation and is in good agreement with the freezing
$\alpha_s$ behaviour.
