Through the theoretical analysis and research works on some famous mining algorithms, a new mining algorithm named Cherry is proposed in this paper. It bases on FP-tree technology and adopts a novel Cherry-Items-detecting technology. This novel technology can find those prefixes which result to the unclosed or redundant frequent itemsets without maintaining the frequent closed itemsets mined so far in the main memory. In the performance test, the Cherry algorithm is compared with other state of the art algorithms, such as FP-CLOSE, LCMv2 and DCI-CLOSE, in many synthetic and real data sets. The experimental results demonstrate that the Cherry algorithm outperforms them in low support.