Large-eddy simulation of a supersonic hydrogen-air non-premixed lifted jet flame is reported in the configuration studied by Cheng et al. (1994). The emphasis of the study is on the mechanism driving flame stabilization. The resolution issue is first addressed by considering three meshes of, respectively, 4, 32 and 268 millions of cells. The highest resolution of 60 mu m allows for resolving the flame with a reduced chemical kinetics. LES results are found in good agreement with experimental data and previous simulations of the literature. It is observed in the simulations that the highly unstable flame base exhibits a cyclic period of around 0.25 ms, with the transient occurence of shock diamonds. These shocks may enhance the mixing of the reactants and control the autoignition processes occurring in the vicinity of the burner exit. The flame also exhibits a transient bow shock shape structure. The dynamics of the turbulent flame base, and the fluctuations of its streamwise position, thus appears to be controlled by the intricate coupling between autoignition and the upstream propagation of strong pressure waves sustained by combustion, pertaining to an intermittent detonation-like mechanism. From these highly resolved unsteady simulations, a scenario is drawn to explain the cyclic time evolution of the structure of the unsteady turbulent flame base, in direct relation with its fluctuating streamwise position. (C) 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.