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We find polynomial-type Jost solution of the self-adjoint discrete Dirac systems. Then we investigate analytical properties and asymptotic behaviour of the Jost solution. Using the Weyl compact perturbation theorem, we prove that discrete Dirac system has the continuous spectrum filling the segment [-2,2]. We also study the eigenvalues of the Dirac system. In particular, we prove that the Dirac system has a finite number of simple real eigenvalues.

Jost Solution and the Spectrum of the Discrete Dirac Systems