  The Hadron Resonance Gas Model with two chemical freeze-outs, connected by
conservation laws is considered. We are arguing that the chemical freeze-out of
strange hadrons should occur earlier than the chemical freeze-out of
non-strange hadrons. The hadron multiplicities measured in the heavy ion
collisions for the center of mass energy range 2.7 - 200 GeV are described well
by such a model. Based on a success of such an approach, a radical way to
improve the Hadron Resonance Gas Model performance is suggested. Thus, we
suggest to identify the hadronic reactions that freeze-out noticeably earlier
or later that most of the others reactions (for different collision energies
they may be different) and to consider a separate freeze-out for them.
