The formation of a graphene-like AlN (g-AlN) layer on a (111) oriented silicon substrate in ammonia molecular beam epitaxy (MBE) has been investigated by the RHEED method. A flat AlN layer with a thickness of a few monolayers was formed by the deposition of Al atoms onto a highly ordered SiN-(8 x 8) surface prepared on the atomically flat (111)Si substrate under an ammonia flux. An unusual (4 x 4) structure of g-AlN on the Si surface was found. The exact coincidence of the fundamental (0 1) AlN streak and the fractional-order (0 5/4) beam of the (4 x 4) RHEED structure allows us to measure precisely the in-plane lattice parameters of g-AlN. The g-AlN lattice constant 3.08 angstrom is found in a good agreement with the oh initio calculations performed recently. The evolution of the g-AlN in-plane lattice constant during the initial stages of the g-AlN formation and transformation to the bulk wurtzite AlN was analyzed. (C) 2015 Elsevier B.V. All rights reserved.