An interacting-pair model is considered to attain a new natural orbital functional (NOF). The new approach, which will be termed PNOF6, belongs to the [Formula: see text]-only family of NOFs known in the literature as PNOFi. Accordingly, the approximated two-particle reduced density matrix (RDM) is reconstructed from the one-particle RDM, considering an explicit form of the two-particle cumulant in terms of the occupation numbers, and enforcing (2,2)-positivity conditions for the N-representability of the 2-RDM. PNOF6 is superior to its predecessor, PNOF5, which is an independent-pair approach. The functional is able to treat both dynamic and static correlations, thereby putting together the advantages of the other members of this series. The theory is applied to the dissociation of selected diatomic molecules. The equilibrium distances, dipole moments, harmonic frequencies, anharmonicity constants, and binding energies of the considered molecules are presented. Comparative potential energy curves for the deformation of benzene are given at the PNOF5 and PNOF6 levels of theory. In benzene, PNOF5 breaks the symmetry by about 1.5°, with an energy lowering of almost 3 kcal/mol, whereas PNOF6 provides the correct D6h symmetry.