The structural behaviour of both low-temperature beta- and high-temperature alpha -Ba(OD)(2), barium dihydroxide-d, was investigated at temperatures between 10 and 552 K by neutron powder diffraction. While the beta phase (P2(1)/n) remains stable to the lowest temperature investigated, the quenchable alpha phase (Pnma) shows a reversible orthorhombic-to-monoclinic phase transition between 100 and 150 K. The structure of the new alpha (m) phase (P2(1)/n) is quite similar to that of the alpha phase. This behaviour is unusual as a metastable phase transforms to another metastable phase. The Pnma <-> P2(1)/n low-temperature phase transition is driven by an order-disorder mechanism, mainly caused by one of the D atoms, which is disordered on positions off the mirror plane, mimicking a special position on the mirror plane in the orthorhombic phase. Refinements of the alpha phase above the phase transition indicate this disorder across the mirror plane through a conspicuously high isotropic displacement parameter if compared to the other D atoms. At low temperature the energy of the vibration is lowered and the D atom is frozen at a general position in a correlated way, thus violating the mirror plane and reducing the space-group symmetry.