In order to improve the unitarity of the S-matrix, an improved variational formulism is derived by proposing new generating functionals and adopting proper asymptotic boundary conditions for trial relative wave functions. The formulas with the weighted line-column balance for the single-channel and multi-channel scatterings, where the non-central interaction is implicitly considered, are presented. A numerical check is performed with a soluble model in a four coupled channel scattering problem. The result shows that the high accuracy and the unitarity of the S-matrix are reached.
