The exchange part of the usual Hartree-Fock potential in the unrestricted Hartree-Fock (UHF) theory is suitablyaveraged to construct an, average one-electron model Hamiltonian which generates a set of spin-restricted one-electron orbitals in a self-consistent manner. These orbitals are then used to calculate the electronic energy of the open-shell system by using the proper functional form for the energy which handles the exchange terms correctly. The eigenvalues ofFav can be used for calculating either the spin-polarised or spin-averaged ionisation potentials of different orbitals at theKoopmans’ theorem level of approximation. Comparison ofEac with the UHF-energy shows thatEUHF<Eac in each case revealing some kind of an upper bound nature ofEac. An approximate variational argument is given. Relationship of our model with the hyper-Hartree-Fock theory of slater is explored and the general problem of eliminating ‘self-interaction’ terms in average Fock-operator based theories is discussed.