The standard formula for the expectation value ( 2 of the total spin operator for single determinant wave functions is transformed to a form in which it appears a physically reasonable sum of atomic and diatomic contributions. The result obtained is much similar to that of previous treatments of local spins, but is free from their difficulty: it does not assign any spins to the atoms in molecules treated by the closed shell RHF method. (c) 2007 Elsevier B.V. All rights reserved.