We prove that Mayer's recent proposition [I. Mayer, Chem. Phys. Lett. 437 (2007) 284] to consider the singular-value decomposition of the CIS coefficient matrix of an excited state leads to the natural orbitals of that state. It also follows that the CIS natural orbitals emerge by separate unitary transformations in the occupied and virtual Hartree-Fock subspaces. (C) 2007 Elsevier B.V. All rights reserved.