The molecular orbitals for B4H4, B4F4, B4Cl4, B4Br4 and B4I4 have been calculated by using all-electron or effective core potential ab initio method at the self-consistent field level using basis sets with diffuse and polarization functions. The boron-boron and boron-halide (-hydrogen) distances of these cage compounds are optimized with three kinds of basis sets constrained to a tetrahedral symmetry. According to the localization scheme of Boys, four three-centered two-electron (3c2e) B-B-B bonds localized on each of the faces of the B4 tetrahedron are derived for B4X4 clusters. The HOMO-LUMO energy gaps, atomization energies and Mulliken overlap populations of these compounds indicate that the stabilities of the clusters decrease in the sequence of B4F4 > B4Cl4, B4H4 > B4Br4 > B4I4. The molecular orbitals for B4H4, B4F4, B4Cl4, B4Br4 and B4I4 have been calculated by using all-electron or effective core potential ab initio method at the self-consistent field level using basis sets with diffuse and polarization functions. The boron-boron and boron -halide (-hydrogen) distances of these cage compounds are optimized with three kinds of sets of constrained to a tetrahedral symmetry. According to the localization scheme of Boys, four three-centered two-electron (3c2e) BBB bonds localized on each of the faces of the B4 tetrahedron are derived for B4X4 clusters. The HOMO-LUMO energy gaps, atomization energies and Mulliken overlap populations of these compounds indicate that the stabilities of the clusters decrease in the sequence of B4F4> B4Cl4, B4H4> B4Br4> B4I4.