Abstract
A Löwdin projected Slater determinant with different orbitals for different spin is an element of an f(S, N) dimensional space spanned by a set of linearly independent eigenfunctions of Ŝ2 generated from the Slater determinant. A basis for this space is the set of valence-bond functions obtainable from the given Slater determinant. The decomposition of a projected determinant in terms of the valence-bond basis is determined for the singlet case. Possible applications of the decomposition are discussed.