We have made time-of-flight neutron diffraction measurements on α-manganese metal. Powder diffraction measurements were made at 14 temperatures between 15 and 305 K, and single crystal measurements were made at 15 and 300 K. We found that the crystal structure of α-Mn is tetragonal below its Néel point of 100 K, with crystal symmetry I4̄2m and magnetic (Shubnikov) symmetry PI4̄21c. In agreement with the earlier results of Yamada et al., there are six independent magnetic atoms, and we found that their moments are weakly temperature dependent. The onset of magnetic order causes slight changes in the atomic positions and in the average atomic elastic constant.