A hyperclique pattern [12] is a new type of association pattern that contains items which are highly affiliated with each other. More specifically, the presence of an item in one transaction strongly implies the presence of every other item that belongs to the same hyperclique pattern. In this paper, we present a new algorithm for mining maximal hyperclique patterns, which are desirable for pattern-based clustering methods [11]. This algorithm exploits key advantages of both the Depth First Search (DFS) strategy and the Breadth First Search (BFS) strategy. Indeed, we adapt the equivalence pruning method, one of the most efficient pruning methods of the DFS strategy, into the process of the BFS strategy. As demonstrated by our experimental results, the performance of our algorithm can be orders of magnitude faster than standard maximal frequent pattern mining algorithms, particularly at low levels of support.