We propose a new algorithm for computing recursive closures. The main idea behind this algorithm is tree labeling and graph decomposition, based on which the transitive closure of a directed graph can be computed in O(e/spl middot/d/sub max//spl middot/d/sub out/) time and in O(n/spl middot/d/sub max//spl middot/d/sub out/) space, where n is the number of the nodes of the graph, e is the numbers of the edges, d/sub max/ is the maximal indegree of the nodes, and d/sub out/ is the average outdegree of the nodes. Especially, this method can be used to efficiently compute recursive relationships of a directed graph in a relational environment.