The B4N4 configurations were designed by using the molecular figure software. The full geometry optimization and harmonic vibration frequency analysis were performed at the 6-31G(d) level using density functional theory B3LYP method,which indicates that the five isomers are stationary points on the potential energy surface of B4N4 molecules. The geometry structure,frontier molecular orbital (FMO) and mulliken population have been analyzed. The bonding properties and hybrid type were also discussed in detail,showing the addition of hydrogen atoms to boron or nitrogen atom would increase the stabilities of the BN clusters. The full geometry optimization and harmonic vibration frequency analysis were performed at the 6-31G (d) level using density functional theory B3LYP method, which indicates that the five isomers are stationary points on the The energy structure of B4N4 molecules. The geometry structure, frontier molecular orbital (FMO) and mulliken population have been analyzed. The bonding properties and hybrid type were also discussed in detail, showing the addition of hydrogen atoms to boron or nitrogen atom would increase the stabilities of the BN clusters.