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Decomposing a query window into maximal quadtree blocks is a fundamental problem in quadtree-based spatial database. Recently, Proietti presented the first optimal algorithm for solving this problem. Given a query window of size n1×n2, Proietti's algorithm takes O(n1) time, where n1=max(n1, n2). Based on a strip-splitting approach, we present a new optimal algorithm for solving the same problem. Experimental results reveal that our proposed algorithm is quite competitive with Proietti's algorithm.