  We show that the real parts of diagonal matrix elements of the exact
effective Hamiltonian governing the time evolution in the subspace of states of
neutral kaons and similar particles can not be equal for $t > t_{0}$ ($t_{0}$
is the instant of creation of the pair $K_{0}, {\bar{K}}_{0}$) when the total
system under consideration is CPT invariant but CP noninvariant. The unusual
consequence of this result is that, contrary to the properties of stable
particles, the masses of the unstable particle, e.g.. $K_{0}$, and its
antiparticle, ${\bar{K}}_{0}$, need not be equal for $t \gg t_{0}$ in the case
of preserved CPT and violated CP symmetries.
