High-resolution photoluminescence spectra have been measured in high-quality homoepitaxial GaN grown on a free-standing GaN substrate with lower residual strain than in previous work. Unusually strong and well-resolved excitonic lines were observed. Based on free-and bound exciton transitions some important GaN parameters are derived. The Arrhenius plot of the free A exciton recombination yields a binding energy of 24.7 meV. Based on this datum, an accurate value for the band-gap energy, E G ͑4.3 K͒ ϭ 3.506 eV, can be given. From the donor bound excitons and their ''two-electron'' satellites, the exciton localization energy and donor ionization energy are deduced. Finally, estimates of the electron and hole masses have been obtained within the effective mass approximation.