We investigate whether the natural orbitals (NOs) minimize parallel to Psi - Phi parallel to(2), where Psi is a wave function and Phi is a full configuration interaction (CI) approximation to Psi in a reduced basis. We will show that the NOs rarely provide the optimal orbitals for Phi, except when (1) there are only two particles or (2) only one basis function is removed in the case of fermions. Further, we will show that the CI expansion coefficients of Psi and Phi are identical up to a global scaling factor and demonstrate how the NOs can be used to generate the orbitals that minimize parallel to Psi - Phi parallel to(2). (C) 2013 Elsevier B.V. All rights reserved.