We considered the properties of the fluorescence anisotropy when the cylindrical symmetry of the fluorescence emission field is absent due to the effects of polarized light quenching. By light quenching we mean stimulated emission by a second longer wavelength pulse following the excitation pulse. In these experiments one observes the excited state population which remains following stimulated emission. When cylindrical symmetry is not present the generally known definition of the emission anisotropy cannot be applied. A generalized theory of anisotropy was described previously by Jablon´ski. However, we found this formalism to be inadequate for the expected experimental results of light quenching. An extension of this concept, which we call an anisotropy vector, appears capable of describing the expected orientation under all conditions of light quenching. We found that the anisotropy vector can exist within a plane defined by two projections r(H) and r(V). The projection r(V) is comparable to the classical steady state or time-dependent anisotropy with cylindrical symmetry. The projection r(H) has no direct analogue in classical anisotropy theory. The interesting behavior of the anisotropy vector is that all possible points (r(H),r(V)) are placed inside a certain triangle, which we call a triangle of anisotropy. For symmetrical molecules, or for molecules which display isotropic depolarizing rotations, the anisotropy vector is expected to decay on the anisotropy triangle along straight lines towards the origin. The concept of the anisotropy vector should allow predictions of the effect of polarized light quenching on the anisotropy decays, and suggests experimental methods to study anisotropy decays in the presence of light quenching. Further work is needed to apply these concepts to anisotropic rotators.