  The exact exponential Foldy-Wouthuysen transformation operator applicable for
a particle with an arbitrary spin is derived. It can be successfully utilized
for verifying any Foldy-Wouthuysen transformation method based on the
exponential operator. When a verified method is relativistic, the relativistic
exponential operator should be expanded in the semirelativistic power series.
The use of the obtained exponential operator for a derivation of the
Foldy-Wouthuysen Hamiltonian makes it possible to check the validity of any
other method of the Foldy-Wouthuysen transformation, while this possibility may
need a greater computational effort.
