The Lagrangian matrix of the density matrix functional theory (DMFT) is shown to be identical with the generalized Fock matrix that enters the extended Koopmans' theorem (EKT), opening an avenue to computations of ionization potentials that avoids multiple energy-difference calculations. The performance of this new DMFT-EKT formalism is demonstrated with the 'primitive' DMFT functionals as an example. (c) 2005 Elsevier B.V. All rights reserved.