Spatial data often possess multiple components, such as local clusters and global clustering, and these effects are not easy to be separated. In this study, we propose an approach to deal with the cases where both global clustering and local clusters exist simultaneously. The proposed method is a two-stage approach, estimating the autocorrelation by an EM algorithm and detecting the clusters by a generalized least square method. It reduces the influence of global dependence on detecting local clusters and has lower false alarms. Simulations and the sudden infant disease syndrome data of North Carolina are used to illustrate the difference between the proposed method and the spatial scan statistic.