AIN thin films, grown on (0001) sapphire substrates by molecular beam epitaxy (MBE), were annealed at high temperature (up to 1650 degrees C) in flowing N-2. X-ray diffraction (XRD) studies, combined with Williamson-Hall and Srikant plots, have shown that annealing leads to a strong reduction of both edge and mixed threading dislocation densities, as confirmed by transmission electron microscopy (TEM) images, up to 75%. Moreover, it is found that annealing at high temperatures allows the relaxation of the tensile strain in the AIN film due to the growth process. In addition, the morphological properties of the films were determined by atomic force microscopy (AFM) and show that the annealing conditions have a strong impact on the surface morphology and roughness. Finally, an annealing at 1550 degrees C for 20 min appears as an ideal tradeoff to enhance the structural properties while preserving the initial AIN surface morphology.