The geometries, electronic states, vibrational spectra and thermodynamic properties for (HAINH)n clusters with n=1-15 have been investigated using the ab initio DFT/B3LYP method with basis sets 6-31G* and their ground state structures obtained. Comparison of the (HAINH)n with (AIN)n clusters shows that the skeletons of (HAINH)n consist of four-membered and six-membered rings made of AI-N bonds, and either Al or N atom forms four bonds in which three ones are AI-N bonds and the rest is AI-H or N-H bond.The number of AI-N bonds of (HAINH)n is equal to that of (AIN)n. The magic number regularity of (HAINH)n is n =2, 4,6, 8, etc., all of which are even numbers. ``