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D-Stream algorithm is an extended grid-based clustering algorithm for the data streams. Actually, grid-based clustering can be considered to be a combinatorial problem of the grids and DNA computing techniques are more suitable to solve the combinatorial problem since its first application, which is the Hamilton path problem. In this paper, we propose a new strategy to do CLIQUE clustering using DNA computing techniques and a new framework based on the mobile agent in order to save time and space. The parallelism of DNA computing, the flexibility, autonomy and interaction of the mobile agent improve the executing efficiency of the data streams clustering.