In this work, we have explored new stable structures of the Au-32(Z) (Z = + 1, 0, -1) clusters. Theoretical calculations using density functional theory within the generalized-gradient approximation were performed. Our results show that, in the anion state (Au-32(-)), low-symmetry (disordered) structures are preferred over the caged fullerene-like isomer. In addition, the cationic cluster (Au-32(+)) also exhibits a disordered low-symmetry structure as its lowest energy configuration, but it is much closer in energy to the fullerene-like isomer. These results, obtained at T = 0 K, indicate that disordered structures for the Au-32(-) and AU(32)(+) clusters may be detected not only at room temperature, as was experimentally verified for the Au-32(-) one, but also at much lower temperatures.