The structure of aluminium bromide has been reinvestigated by X-ray diffraction in three different ways: (a) on a single crystal grown in a glass capillary, (b) on powder in a Debye-Scherrer glass capillary and (c) on an area of powder placed in a protective container for Bragg-Brentano geometry. In accordance with previous results, the structure belongs to the monoclinic space group P2(1)/a, no. 14, C-2h(5), with a = 10.301(4), b = 7.095(2), c = 7.525(3) Angstrom, and beta = 96.44(3)degrees, and with two Al2Br6 molecules per unit cell. The single crystal was refined to R = 0.0746. Rather similar structural results were obtained from full-profile Rietveld refinements of powder data [goodness of fit = 1.38 and 2.54 for (b) and (c), respectively]. The Al2Br6 molecule consists of two edge-sharing, almost regular AlBr4 tetrahedra. The Al-Br bond distances are in the range 2.21-2.42 Angstrom, in accordance with what should be expected from related structure determinations.