The Piris Natural Orbital Functional, in its 5th version (PNOF5), has been used to obtain the localized bonding picture of methane that agrees well with the Pauling proposition of hybrid orbitals, and to predict the two-peak structure of its vertical valence ionization energy spectrum. The ionization energies have been calculated using the extended Koopmans’ theorem. The calculated PNOF5 values are in good agreement with the corresponding experimental data. It is demonstrated that it is possible to reconcile sp3 orthogonal hybrid orbitals with the experimental vertical ionization energies observed for the CH4 within the framework of the natural orbital functional theory.