Most algorithms for mining spatial co-locations adopt an Apriori-like approach to generate size-k prevalence co-locations after size-(k - 1) prevalence co-locations. However, generating and storing the co-locations and table instances is costly. A novel order-clique-based approach for mining maximal co-locations is proposed in this paper. The efficiency of the approach is achieved by two techniques: (1) the spatial neighbor relationships and the size-2 prevalence co-locations are compressed into extended prefix-tree structures, which allows the order-clique-based approach to mine candidate maximal co-locations and co-location instances; and (2) the co-location instances do not need to be stored after computing some characteristics of the corresponding co-location, which significantly reduces the execution time and space required for mining maximal co-locations. The performance study shows that the new method is efficient for mining both long and short co-location patterns, and is faster than some other methods (in particular the join-based method and the join-less method).