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Gallup has recently given a solution to the problem of determining an orthogonal representation matrix for an arbitrary permutation of the symmetric group in terms of sandwich representations. In this paper it is shown how this provides a means for the precalculation and storage of the necessary distinct coefficients needed in the construction of the various Hamiltonian matrix elements of an orthogonal orbital CI calculation. This method has the advantage over those published previously in that the spin degeneracy problem is handled more efficiently. It is shown that this procedure can be utilized with both the "construction and storage" algorithms and, also, the recently developed "direct vector" methods when dealing with large Hamiltonian matrices. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.