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Many existing grid authorization systems adopt an inefficient structure of storing security policies for the available resources. That leads to huge repetitions in checking security rules. One of the efficient mechanisms that handles these repetitions is the Hierarchical Clustering Mechanism (HCM). HCM reduces the redundancy in checking security rules compared to the Brute Force Approach as well as the Primitive Clustering Mechanism (PCM). However, HCM is not totally free from redundancy. In this paper, new HCM tree-building algorithms are proposed which further reduce the redundancy and increase the efficiency to a reasonable extent.