  A recently formulated version of the eigenchannel method [R. Szmytkowski,
Ann. Phys. (N.Y.) {\bf 311}, 503 (2004)] is applied to quantum scattering of
Schr\"odinger particles from non-local separable potentials. Eigenchannel
vectors and negative cotangents of eigenphase-shifts are introduced as
eigensolutions to some weighted matrix spectral problem, without a necessity of
prior construction and diagonalization of the scattering matrix. Explicit
expressions for the scattering amplitude, the total cross section in terms of
the eigenchannel vectors and the eigenphase-shifts are derived. An illustrative
example is provided.
