[en] The low-energy limit of the Bethe-Salpeter equation with a relativistic kernel for quark-antiquark bound states is considered. It is shown that this limlt as equivalent to a localization of the potential which becomes a special 4-quark Nambu-Jona-Lasinio one. The mass spectrum of the low-lying mesons is calculated without expanding in energy. Thereby the S-V, P-A and V-T mixings are taken into account exactly. Furthermore the pion decay constant is determined. We received good agreement with the experimental data