  The projected random phase approximation (PRPA) for charge-exchange
excitations is derived from the time-dependent variational principle. Explicit
results for the unperturbed energies (including the self-energy corrections),
the PRPA matrices, and the transition matrix elements are presented. The effect
of the projection procedure on the two-neutrino $\beta\beta$ decay in $^{76}Ge$
is briefly discussed.
