  Relativistic wave equation of motion without redundant components for the
particle having spin 3/2 has been considered. In order to show the newness a
comparison with the known equations for the spin s=3/2 field is given.
Therefore, the brief review of the relativistic wave equations for the particle
with spin s=3/2 is given. In our equation the wave function for the
particle-antiparticle doublet has only 8 components. The consideration is
carried out both at the level of relativistic quantum mechanics and at the
level of local field theory. The extended Foldy--Wouthuysen transformation,
which gives the operator link between these two levels is suggested.
