We have determined the structures of two phases of unsolvated Mg(BH(4))(2), a material of interest for hydrogen storage. One or both phases can be obtained depending on the synthesis conditions. The first, a hexagonal phase with space group P6(1), is stable below 453 K. Upon heating above that temperature it transforms to an orthorhombic phase, with space group Fddd, stable to 613 K at which point it decomposes with hydrogen release. Both phases consist of complex networks of corner-sharing tetrahedra consisting of a central Mg atom and four BH(4) units. The high-temperature orthorhombic phase has a strong antisite disorder in the a lattice direction, which can be understood on the basis of atomic structure.