  The Foldy-Wouthuysen transformation (FWT) is used to separate distinct
components of relativistic spinor field, e.g. electron and positron. Usually,
the FWT is perturbative, but in some cases there is an involution operator and
the transformation can be done exactly. We consider some aspects of an exact
FWT and show that, even if the theory does not admit an involution operator,
one can use the technique of exact FWT to obtain the conventional perturbative
result. Several particular cases can be elaborated as examples.
