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