Evolution of the step arrangement on vicinal (0001) surfaces of an α-alumina crystal annealed for 1h in the range of 1000-1500 o C in air was investigated by atomic force microscopy. For T<1200 o C, coalescence of monosteps (h 1 =0.2nm) forms mainly parallel double-height steps. At temperatures >1200 o C, steps with larger heights grow either due to direct coalescence or due to the displacement of single steps. During coalescence of steps in the whole temperature range investigated, the direction of the higher steps keeps parallel to that of the initial monosteps over hundreds of microns although it does not correspond to any low index crystalline orientation. Different mechanisms of growth of the steps are discussed. A quantitative estimation of the activation energy of one effective self diffusion process can be performed.