The optically detected electron paramagnetic resonance (ODMR) spectrum of self-trapped excitons (STEs) in NaBr was measured using a microwave frequency of 25.9 GHz and compared with that measured previously at 24.0 GHz. In lock-in detected ODMR only one structureless non-Gaussian line was observed for each frequency. From the field positions of the lines obtained in the previous and new measurements a zero-field splitting of D = 1.7 T was derived. On the basis of transient ODMR measurements in KBr it is shown that the shape of the ODMR line does not follow the -centre nuclear spin statistics of the STE because of the dependence of the lifetimes on the nuclear spin states. Similar effects seem to occur in all alkali bromides.