High reflectivity and crack-free ultraviolet distributed Brago, reflectors (DBRs), based on AlGaN/ AIN quarter-wave layers, have been designed and grown on (0001) sapphire by plasma-assisted molecular beam epitaxy. To minimize the tensile stress and thus prevent nucleation and propagation of cracks in the DBRs, the substrate was coated first with an AIN film, of thickness approximately equal to the total thickness of all the AIN layers in the epitaxially grown DBR structure. In such a configuration the AIN layers are stress-free, while the AlGaN layers are under compressive stress. Peak reflectivity higher than 99% was obtained in all samples. The design calculations and simulations of measured reflectivity data were performed using the transmission matrix method. The measured reflectivity spectra have a bandwidth of around 20% smaller than the simulated spectra, a result attributed to a combination of changes of the thickness and variations in the Al content in the quarter-wave layers.