Using density functional theory (DFT), we have systematically calculated the equilibrium geometries, electronic structure, and electron detachment energies of Al(BH4)(n=1 -> 4) and Al(BF4)(n=1 -> 4) at the B3LYP/6-311+G(2d,p) level of theory. The electron affinities of Al(BH4)(n) not only exhibit odd-even alternation, just as seen in (BH4)(n), but also, for n = 3 and 4, show a remarkable behavior: whereas the electron affinities of BH3 and BH4 are, respectively, 0.06 and 3.17 eV, those of Al(BH4)(3) and Al(BH4)(4) are 0.71 and 5.56 eV. Results where H is replaced by F are also very different. The electron affinities of BF3 and BF4 are, respectively, -0.44 and +6.86 eV, and those of Al(BF4)(3) and Al(BF4)(4) are 1.82 and 8.86 eV. The results demonstrate not only marked difference when H is replaced by F but also substantially enhanced electron affinities by almost 2 eV when BH4 and BF4 units are allowed decorate a metal atom, confirming the recently observed hyperhalogen behavior of superhalogen building blocks.