Superhalogens are species whose electron affinity (EA) or vertical detachment energy (VDE) exceed to those of halogen. These species typically consist of a central electropositive atom with electronegative ligands. The EA or VDE of species can be further increased by using superhalogen as ligands, which are termed as hyperhalogen. Having established BH4- as a superhalogen, we have studied BH4-x(BH4)x- (x = 1 to 4) hyperhalogen anions and their Li-complexes, LiBH4-x(BH4)x using density functional theory. The VDE of these anions is larger than that of BH4-, which increases with the increase in the number of peripheral BH4 moieties (x). The hydrogen storage capacity of LiBH4-x(BH4)x complexes is higher but binding energy is smaller than that of LiBH4, a typical complex hydride. The linear correlation between dehydrogenation energy of LiBH4-x(BH4)x complexes and VDE of BH4-x(BH4)x- anions is established. These complexes are found to be thermodynamically stable against dissociation into LiBH4 and borane. This study not only demonstrates the role of superhalogen in designing new materials for hydrogen storage, but also motivates experimentalists to synthesize LiBH4-x(BH4)x (x = 1 to 4) complexes.