  The spin 3/2 fermion models with contact interactions have a {\it generic}
SO(5) symmetry without any fine-tuning of parameters. Its physical consequences
are discussed in both the continuum and lattice models. A Monte-Carlo algorithm
free of the sign problem at any doping and lattice topology is designed when
the singlet and quintet interactions satisfy $U_0\le U_2\le -{3\over5} U_0
(U_0\le 0)$, thus making it possible to study different competing orders with
high numerical accuracy. This model can be accurately realized in ultra-cold
atomic systems.
