In this paper we propose a discretisation scheme for asymptotically stable homogeneous systems. This scheme exploits the information provided by a homogeneous Lyapunov function of the system. The main features of the scheme are: 1) the dis-cretisation method is explicit and; 2) the discrete-time system preserves the asymptotic stability, the convergence rate, and the Lyapunov function of the original continuous-time system.