A non Hermitian fermion model containing a γ 5 matrix in the mass term m m 1 + γ 5 m 2 is con sidered. A new refined condition of the unbroken ᏼsymmetry of the theory is proposed that comprises an indication that the initial domain of unbroken ᏼsymmetry is divided into subdomains corresponding to the description of ordinary and exotic particles. A relationship is established between the theory under study and the quantum field theory with maximal mass M developed on the basis of the geometric approach. The operator Ꮿ is calculated explicitly, which is required for the construction of a new scalar product in the theory with a non Hermitian Hamiltonian.

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