The new double-cation Al-Li-borohydride is an attractive candidate material for hydrogen storage due to a very low hydrogen desorption temperature (~70 °C) combined with a high hydrogen density (17.2 wt %). It was synthesised by high-energy ball milling of AlCl₃ and LiBH₄. The structure of the compound was determined from image-plate synchrotron powder diffraction supported by DFT calculations. The material shows a unique 3D framework structure within the borohydrides (space group=P-43n, a=11.3640(3) Å). The unexpected composition Al₃Li₄(BH₄)₁₃ can be rationalized on the basis of a complex cation [(BH₄)Li₄]³⁺ and a complex anion [Al(BH₄)₄]^-. The refinements from synchrotron powder diffraction of different samples revealed the presence of limited amounts of chloride ions replacing the borohydride on one site. In situ Raman spectroscopy, differential scanning calorimetry (DSC), thermogravimetry (TG) and thermal desorption measurements were used to study the decomposition pathway of the compound. Al-Li-borohydride decomposes at ~70 °C, forming LiBH₄. The high mass loss of about 20 % during the decomposition indicates the release of not only hydrogen but also diborane.