Multi-quark interactions with a globally stable vacuum

It is shown that $U(3)_L\times U(3)_R$ eight-quark interactions stabilize the asymmetric ground state of the well-known model with four-quark Nambu -- Jona-Lasinio and six-quark 't Hooft interactions. The result remains when the reduced SU(3) f\mbox{}lavour symmetry is explicitly broken by the general current quark mass term with $\hat{m}_u\neq\hat{m}_d\neq\hat{m}_s$.