It is known that, in the case of self-conjugate distinct eigenvalue spectra, the closed-loop eigen-structure assignable by output feedback in constrained by the requirement that the loft and right eigenvectors be in certain subspaces. In this paper an algorithm is presented which can be used to select these left and right eigenvectors in the case in which the number of inputs plus the number of outputs exceeds the number of states. The algorithm is ideally suited to digital computer implementation and an ALGOL program for this is available.