  In this work we show that the existence of a complete biorthonormal set of
eigenvectors of the effective Hamiltonian governing the time evolution of
neutral meson system is a necessary condition for diagonalizability of such a
Hamiltonian. We also study the possibility of probing the $CPT$ invariance by
observing the time dependence of cascade decays of type
$P^{\circ}(\bar{P^{\circ}})\to \{M_a,M_b\}X\to fX$ by employing such basis and
exactly determine the $CPT$ violation parameter by comparing the time
dependence of the cascade decays of tagged $P^{\circ}$ and tagged
$\bar{P^{\circ}}$.
