In this paper, a new innovative method for approximating fractional order system by an integer order model is proposed. The Riemann-Liouville's integral is adopted for fractional order operations via block pulse expansion and a new SID (system identification) matrix can be derived to identify the coefficients of an integer order transfer function to approximate the given fractional order system. In comparison with previous approach via PSO (Particle Swarm Optimization) method, this new approach provides a more reasonable approach and yield better results. Several examples are illustrated to validate our better results.