Rather than rotate one set of orbitals (as in Method #1), as shown by Sundstrom and Head-Gordon, the better approach is to rotate both sets of orbitals (those at the current and previous geometries) so as to generate a fully biorthogonal basis set. Such an approach has been used previously for several electronic structure calculations, and significantly generalized by Burton. Here we apply this technique to calculate the singly-excited state overlap matrix for use in non-adiabatic dynamics.