This article deals with the analysis of the time discretization of the supertwisting algorithm, with an implicit Euler method. It is shown that the discretized system is well posed. The existence of a Lyapunov function with convex level sets is proved for the continuous-time closed-loop system. Then, the global asymptotic Lyapunov stability of the unperturbed discrete-time closed-loop system is proved. The convergence to the origin in a finite number of steps is proved also in the unperturbed case. Numerical simulations demonstrate the superiority of the implicit method with respect to an explicit discretization with significant chattering reduction.