  $S=3/2$ system with general isotropic nearest-neighbor exchange within a
mean-field approximation possesses a magnetically ordered ferromagnetic state
and antiferromagnetic state, and two different spin nematic states, with zero
spin expectation values. Both spin nematic phases display complicated symmetry
break, including standard rotational break described by the vector-director
$\vec {u}$ and specific symmetry break with respect to the time reversal. The
break of time reversal is determined by non-trivial quantum averages cubic over
the spin components and can be described by unit "pseudospin" vector $\vec
{\sigma}$. The vectors $\vec {\sigma}$ on different sites are parallel for a
nematic state, and $\vec {\sigma}$'s are antiparallel for different sublattices
for an antinematic phase.

Strongly Correlated Electrons