A new possible explanation is given to the anomalous fading of thermoluminescence (TL), observed in some materials. It is suggested that anomalous fading may, in some cases, be normal fading in disguise. The existence of non-radiative centers which are competing with the radiative luminescence center may cause the occurrence of a very narrow TL peak. The apparent kinetics parameters, say Eapp and sapp in first order kinetics, may appear to be much larger than the real values due to the narrowing of the peak. This, in turn, results in the expectation of a very long decay time, τapp, at, for example, room temperature. The real values of the parameters are, however, such that the loss of trapped carriers is orders of magnitude faster. The details of the model are given in terms of rate equations, as well as examples of numerical solutions during excitation followed by relaxation and then heating during the read-out phase. From these, the effective expected lifetimes were up to five orders of magnitude larger than that of the observable effect, which can explain, at least in some cases, the anomalous fading.