  An application of the new formulation of the eigenchannel method [R.
Szmytkowski, Ann. Phys. (N.Y.) {\bf 311}, 503 (2004)] to quantum scattering of
Dirac particles from non-local separable potentials is presented. Eigenchannel
vectors, related directly to eigenchannels, are defined as eigenvectors of a
certain weighted eigenvalue problem. Moreover, negative cotangents of
eigenphase-shifts are introduced as eigenvalues of that spectral problem.
Eigenchannel spinor as well as bispinor harmonics are expressed throughout the
eigenchannel vectors. Finally, the expressions for the bispinor as well as
matrix scattering amplitudes and total cross section are derived in terms of
eigenchannels and eigenphase-shifts. An illustrative example is also provided.
