In this paper, we discuss the implementation of a control system using reference governor for the control of constraint systems. This control scheme uses the maximal output admissible set to determine the reference input r[k] at the time k. When the number of facets of the maximal output admissible set is very large, it might happen that the computing time to determine r[k] exceeds the sampling period. To reduce the computing time, we propose an efficient scheme to determine r[k] using the information of the facet F_ik−1 which is used to determine r[k−1] and the set of facets which are adjacent to F_ik−1 . Set of adjacent facets for every facet of the maximal output admissible set are computed in advance. Moreover, the effectiveness of proposing method is verified by simulation and experiment for a cart system with pendulum.