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An algorithm is presented which uses the channel packet method (CPM) to compute S-matrix elements. The standard approach to solving for the S-matrix elements is to use states which contain only positive or negative momentum. In doing so however, the standard approach fails to produce accurate S-matrix elements at low energies since accurate results are only obtainable over the energy range defined by the states. Therefore, in order to obtain accurate results at low energy one must formulate states which contain both positive and negative momentum. In order to incorporate states which have positive and negative momentum a four-by-four matrix containing the momentum expansion coefficients of the states is introduced. The approach does not consider scattering from one side or the other, rather it considers both incoming and outgoing states from the left and right simultaneously. Therefore, during one simulation all four S-matrix elements are computed.