We present here a study of the growth of AlN by molecular beam epitaxy on sapphire (0 0 0 1) substrates using reflection high energy electron diffraction and atomic force microscopy. The surface morphology and reconstruction have been monitored as a function of temperature using initially nitrided sapphire substrates. We obtained a (2 x 2) reconstruction on AlN after growth using two different procedures; either by cooling or by remaining at high temperature for an extended period of time. During the subsequent growth of AlN we can maintain this (2 x 2) reconstruction for some time, before it reverts to a (1 x 1) pattern. We have also studied the influence upon the reconstruction of post-growth deposition of Al at high temperature onto the AlN surface after growth. By desorbing the excess Al, the (2 x 2) surface reconstruction recovery time was found to be directly proportional to the Al deposition time. This strongly suggests, therefore, that the (2 x 2) reconstruction may be intrinsic to AlN.