Studies throughout the past decade indicate that the mass of the first generation of stars was extremely large, unlike most stars in our galaxy. However, according to recent work on the mass accretion phase, the gas is likely to fragment and produce a cluster of stars, rather than accreting smoothly onto a central star. Furthermore, the calculations by Hosokawa et al show that radiation from the protostar inhibits mass accretion, fuelling discussions on the maximum mass the primary star can achieve. We report the results from three-dimensional radiation hydrodynamic (RSPH) calculations, in which we examined the effect of the dissociation of hydrogen molecules in the mass accretion phase of the primary star.