Low-temperature measurements of transverse magneto-resistance were made on 24 single crystals of pure aluminium in magnetic fields up to 20 kG. In contrast with the theory, neither complete saturation of magneto-resistance nor quadratic variation with field were observed in any orientation. The anisotropy of the magneto-resistance was small, but showed a pattern consistent with symmetry requirements. These results appear inexplicable on a basis of Harrison's four orthogonal plane wave model of the aluminium Fermi surface, but can be explained qualitatively in terms of a slightly different Fermi surface which touches the corners of the second Brillouin zone. This model is not inconsistent with other experimental results.