  We show that the diagonal matrix elements of the effective Hamiltonian
governing the time evolution in the subspace of states of an unstable particle
and its antiparticle need not be equal at $t > t_{0}$ ($t_{0}$ is the instant
of creation of the pair) when the total system under consideration is CPT
invariant but CP noninvariant. To achieve this we use the transition amplitudes
for transitions $|{\bf 1}> \to |{\bf 2}>$, $|{\bf 2}> \to |{\bf 1}>$ together
with the identity expressing the effective Hamiltonian by these amplitudes and
their derivatives with respect to time $t$. This identity must be fulfilled by
any effective Hamiltonian (both approximate and exact) derived for the two
state complex. The unusual consequence of this result is that, contrary to the
properties of stable particles, the masses of the unstable particle "1" and its
antiparticle "2" need not be equal for $t \gg t_{0}$ in the case of preserved
CPT and violated CP symmetries.
