  In e^+e^- annihilation at \sqrt{s}=10.6 GeV Belle Collaboration found, that
J/psi mesons are predominantly produced in association with an extra \bar{c}c
pair. The possible mechanisms of J/psi production are discussed and the
probability of the associate production of \bar{c}c pair is estimated. The
choice between these mechanisms can be done by measuring J/psi polarization. It
is suggested, that in case of heavy ion collisions one may expect remarkable
transverse polarization of produced J/psi, if quark-gluon plasma if formed. The
measurement of asymmetry of e^+e^-(\mu^+\mu^-) angular distribution in J/psi->
e^+e^-(\mu^+\mu^-) decay is a useful tool for detection of quark-gluon plasma
formation in heavy ion collisions.
