  An exact method for direct calculation of the Jost functions and Jost
solutions for non-central potentials which couple partial waves of different
angular momenta is presented. A combination of the variable-constant method
with the complex coordinate rotation is used to replace the matrix
Schr\"odinger equation by an equivalent system of linear first--order
differential equations. Solving these equations numerically, the Jost functions
can be obtained to any desired accuracy for all complex momenta of physical
interest, including the spectral points corresponding to bound and resonant
states. The effectiveness of the method is demonstrated using the Reid
soft-core and Moscow nucleon-nucleon potentials which involve tensor forces.
