  It is pointed out that it is the local symmetry that determines the
realization of the low- and high-spin state of the Co3+ ion. We can rigorously
prove it treating the Co3+ ion as the highly-correlated electron system 3d6,
that fulfiles the Hund's rules with taking into account the spin-orbit
coupling. As the function of the sign of the off-cubic crystal-field distortion
the magnetic or non-magnetic state is realized.
