Extended X-ray absorption fine structure (EXAFS) spectroscopy was used to characterize the (PEO)(n)[ZnBr2(1-x)(LiBr)(x)] system. Values of it and x were chosen so that the average number of nearest-neighbor bromine atoms varied from 2.25 to 3 as determined by Raman spectroscopy. This study determined that the number of nearest-neighbor oxygen atoms was 3, 1, and 0 for zinc with 2, 3, and 4 nearest-neighbor bromine atoms, respectively. Some ambiguity is present in the first case, with four nearest-neighbor oxygen atoms being almost impossible and two being possible but not likely. The mean-squared displacement of the zinc-bromine bond increased almost linearly with absolute temperature, similar to the behavior observed for other covalent or ionic bonds. Interestingly, the strength of the Zn-Br bond, as determined by the change of the mean-squared displacement with temperature, was the same for all samples independent of the degree and nature of coordination. For some samples, there was a clear rise in the mean-squared displacement (MSD) of the Zn-O linkage with temperature. For other samples, the mean-squared displacement at 20 K was extremely large; consequently, the expected increase of the MSD with an increase in temperature was barely noticeable. The MSD Showed a relative minimum at a temperature corresponding roughly to the glass transition temperature for all samples where data were collected in an appropriate temperature range. To our knowledge, this study represents the first time a feature in EXAFS spectra has been found to be sensitive to the glass transition temperature. The significance of this observation in terms of local structural changes at the glass transition is discussed.