In contrast to other III-nitride semiconductors GaN and AlN, the intrinsic (or free) exciton transition in hexagonal boron nitride (h-BN) consists of rather complex fine spectral features (resolved into six sharp emission peaks) and the origin of which is still unclear. Here, the free exciton transition (FX) in h-BN bulk crystals synthesized by a solution method at atmospheric pressure has been probed by deep UV time-resolved photoluminescence (PL) spectroscopy. Based on the separations between the energy peak positions of the FX emission lines, the identical PL decay kinetics among different FX emission lines, and the known phonon modes in h-BN, we suggest that there is only one principal emission line corresponding to the direct intrinsic FX transition in h-BN, whereas all other fine features are a result of phonon-assisted transitions. The identified phonon modes are all associated with the center of the Brillouin zone. Our results offer a simple picture for the understanding of the fundamental exciton transitions in h-BN.