EN
A theoretical analysis is performed of the phenomenon of anisotropic magnetic quenching of a positronium atom formed by polarized positrons in noncubic crystals oriented with respect to an external magnetic field. An initial polarization of positrons is shown to enhance an anisotropy of Ps magnetic quenching and to decrease the strength of magnetic field in which an anisotropy is maximal. A maximal anisotropic effect has been estimated for quasi-Ps in crystalline quartz and Ps complex in naphthalene single crystal.