The methods used till now to calculate the neutrinoless double-beta decay (0νββ decay) matrix elements are the quasiparticle random phase approximation (QRPA), the shell model (SM), the angular momentum projected Hartee–Fock–Bogoliubov approach (HFB) and the interacting boson model (IBM). The different approaches are compared specifically concerning the angular momenta and parities of the neutron pairs, which are changed into two protons by the 0νββ decay. The QRPA and SM involve about the same angular momentum and parity neutron pairs, while the HFB is restricted to 0+, 2+, 4+, … and the IBM to 0+ and 2+ nucleon pairs.