The phase II-P-beta diagram of an easy-plane strongly anisotropic anti
ferromagnet is studied. It is shown that in such a system a realizatio
n of the phase with the nonmagnetic order parameter, the so-called qua
druple phase, is possible. The realization of this phase is caused by
several purely quantum effects, moreover the mechanism of its appearan
ce differs in principle from that of the antiferromagnet or ferromagne
t. The possibility of the disappearance of the angular phase (the so-c
alled quadruple ferromagnetic phase) is also shown.