An adjustable broadening function instead of the conventional Lorentzian one is incorporated in the dielectric function model for hexagonal GaN. One-electron contributions at E 1 critical points and higher-state (mϾ1) exciton terms, which were incorrectly disregarded in the previous study, are taken into account. Model parameters were determined using the acceptance-probability-controlled simulated annealing. As a result, excellent agreement with experimental data for both real and imaginary parts in the range from 1.5 to 10 eV is obtained. Average discrepancy between experimental and calculated data for the real part of the index of refraction equals 2.75ϫ10 Ϫ4 , and for the imaginary part is 1.66ϫ10 Ϫ3 .