  We extend the formalism of the relativistic thermal and kinematic
Sunyaev-Zel'dovich effects and include the polarization of the cosmic microwave
background photons. We consider the situation that a cluster of galaxies is
moving with a velocity \vec{v} with respect to the cosmic microwave background
radiation. In the present formalism, polarization of the scattered cosmic
microwave background radiation caused by the proper motion of a cluster of
galaxies is naturally derived as a special case of the kinematic
Sunyaev-Zel'dovich effect. The relativistic corrections are included also in a
natural way. Our results are in complete agreement with the recent results of
the relativistic corrections obtained by Challinor, Ford and Lasenby with an
entirely different method as well as the nonrelativistic limit obtained by
Sunyaev and Zel'dovich. The relativistic correction becomes to be significant
in the Wien region.
