This paper contains a detailed analysis of the properties of the scalar product of short and long living superpositions of neutral |K₀\rangle , |{\overline {K}}₀\rangle mesons. It is shown for the exact effective Hamiltonian for neutral meson subsystem that the scalar product of its eigenvectors, which correspond with these short and long living superpositions, cannot be real under the assumption of CPT conserved and CP violated. The standard conclusion obtained within the Lee--Oehme--Yang theory of neutral kaons is that in this case such a product should be real. Also, the general and model independent proof that probabilities of transitions |K₀\rangle \rightarrow |{\overline {K}}₀\rangle and |{\overline {K}}₀\rangle \rightarrow |K₀\rangle are not equal in the CP non--invariant system is given.

PACS numbers: 03.65.Ca, 11.10.St, 11.30.Er, 13.20.Eb