Let denote the non-self-adjoint discrete Dirac operator generator in by
where the , , . It is proved that if, for some ,
has a finite number of eigenvalues and spectral singularities (poles of the resolvent kernel which are not eigenvalues), each of finite multiplicity, and continuous spectrum . Under the condition (1) an integral representation is obtained for the Weyl (or, more accurately, the Hellinger-Nevanlinna) function, and this yields an expansion theorem in terms of the principal vectors of .