  We start from a discussion of the general form and general CP-- and CPT--
transformation properties of the Lee--Oehme--Yang (LOY) effective Hamiltonian
for the neutral kaon complex. Next we show that there exists an approximation
which is more accurate than the LOY, and which leads to an effective
Hamiltonian whose diagonal matrix elements posses CPT transformation
properties, which differ from those of the LOY effective Hamiltonian. These
properties of the mentioned effective Hamiltonians are compared with the
properties of the exact effective Hamiltonian for the neutral kaon complex. We
show that the diagonal matrix elements of the exact effective Hamiltonian
governing the time evolution in the subspace of states of an unstable particle
and its antiparticle need not be equal at for $t > t_{0}$ ($t_{0}$ is the
instant of creation of the pair) when the total system under consideration is
CPT invariant but CP noninvariant. 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.
