The dependences on composition of the bond lengths and energy bands of quaternary alloys are calculated on the basis of tight-binding theory under the virtual-crystal approximation. For a quaternary alloy lattice matched to InP, a type II staggered band line-up is observed when the Al composition is larger than 24%. At this point the conduction band discontinuity of heterostructures disappears. The effective electron mass associated with the conduction band minimum is estimated on the basis of the theory, and is in good agreement with the cyclotron resonance experimental results. The relative conduction band discontinuity is determined to be 72.2% for . The band offsets of the related heterojunctions are calculated, and compared with experimental and previous theoretical results.