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According to previous interpretations of experimental data, sodium-scandium double-cation borohydride NaSc(BH4)4 crystallizes in the crystallographic space group Cmcm where each sodium (scandium) atom is surrounded by six scandium (sodium) atoms. A careful investigation of this phase based on ab initio calculations indicates that the structure is dynamically unstable and gives rise to an energetically and dynamically more favorable phase with C2221 symmetry and nearly identical x-ray diffraction pattern. By additionally performing extensive structural searches with the minima-hopping method we discover a class of new low-energy structures exhibiting a novel structural motif in which each sodium (scandium) atom is surrounded by four scandium (sodium) atoms arranged at the corners of either a rectangle with nearly equal sides or a tetrahedron. These new phases are all predicted to be insulators with band gaps of 7.9–8.2 eV. Finally, we estimate the influence of these structures on the hydrogen-storage performance of NaSc(BH4)4.