  In this paper, we find a polynomial-type Jost solution of a self-adjoint
matrix-valued discrete Dirac system. Then we investigate analytical properties
and asymptotic behavior of this Jost solution. Using the Weyl compact
perturbation theorem, we prove that matrix-valued discrete Dirac system has
continuous spectrum filling the segment $[-2,2].$ Finally, we examine the
properties of the eigenvalues of this Dirac system and we prove that it has a
finite number of simple real eigenvalues.
