This article studies Lyapunov stability for nonlinear systems based on discrete-time self-triggered impulsive control (STIC). With the help of comparison approach, some Lyapunov-based sufficient conditions guaranteeing nonZeno behavior and global asymptotic stability of nonlinear systems under STIC are derived. Different from the existing self-triggered mechanisms using implicit expressions to compute the next impulse instant, which may result in computational burden, we propose a novel discrete-time self-triggered mechanism (STM) by which the next impulse instant can be predicted directly by the information of the comparison system. Moreover, the resulting algorithm is easy to be implemented. It is shown that the designed STIC strategy can not only achieve a tradeoff between computational complexity, communication resource usage and control performance, but also has strong robustness and flexibility. Finally, an illustrative simulation is provided showing the effectiveness of the results.