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We generalize a theorem by Khalfin, originally derived for the states $| F_1> = | M^0>$, $| F_2 > = |\bar M^0>$, where $M^0$ is a neutral flavoured meson(e.g., $K^0$ or $B_d^0$), by assuming CPT invariance. Dispensing with CPTinvariance and allowing for an arbitrary pair of orthogonal states $|F_{1,2}>$, we show that any linear combinations $| P_a > = p_a | F_1 > + q_a |F_2>$ and $| P_b > = p_b | F_1 > - q_b | F_2>$, if postulated to beindependently propagating in time, as in the Lee--Oehme--Yang Theory, must bemutually orthogonal. This implies a reciprocity relation: equality of theprobabilities of the transitions $| F_1 > \leftrightarrow | F_2>$. Also impliedis another relation involving the coefficients $p_{a,b}$, $q_{a,b}$, which canbe interpreted as $\mathrm{Im} \theta = 0$, where $\theta$ is therephasing-invariant parameter describing CPT violation in $M^0 \bar M^0$ mixingfor Khalfin's choice of $| F_{1,2}>$. The states $| F_{1,2}>$ of \emph{our}theorem need not form a particle-antiparticle pair, nor even be restricted toparticle physics.Comment: 9 pages, LATEX, no figues. Misprints corrected and part of the  presentation changed, version to be published in Phys. Rev.

Orthogonality of independently propagating states as occurring in the Lee-Oehme-Yang theory