Fermi resonance complicates the vibrational spectrum of the hydroperoxyl radical, HO2. Using a recent three-dimensional potential energy surface, we calculate vibrational wave functions for H-O-16-O-16 and H-O-18-O-18. We identify low-lying Fermi resonant pairs and determine the degree of coupling by constructing linear combinations of these Fermi resonant wave functions. The coefficients are systematically varied to find the linear combination which, through visual inspection, replicates the nodal patterns of "pure" vibrational wave functions. The energies of the pure vibrational levels and the Fermi resonance shifts are also calculated.