The Kohn variational principle (KVP) has been used to compute both the R and the log-derivative matrices, which are formally inverses of one another. We show that the KVP for these matrices are special cases of a KVP for a more general functional which can be derived by imposing more general boundary conditions on the trial function space. This more general matrix, which we denote Z, can then be used to compute the S-matrix in a procedure analogous to that for R and Y. This approach is demonstrated for the Eckart barrier problem. Our studies suggest that within the framework presented, the log derivative case presents some computational advantage.