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A data stream is a massive and unbounded sequence of data elements that are continuously generated at a fast speed. Compared with traditional data mining, knowledge discovery in data streams is more challenging since several requirements need to be satisfied. In this paper we propose a mining algorithm for finding frequent itemsets over a transactional data stream. Unlike most of existing algorithms, our method works based on the theory of Approximate Inclusion-Exclusion to approximate the itemsets' counts. Some techniques are designed and integrated into the algorithm for performance improvement. And the performance of the proposed algorithm is tested and analyzed through several experiments.