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Quantum information processing is in the beginning stages. Among open research problems, quantum circuit synthesis has recently received significant attention. In this paper, we propose a new non-search based moving forward synthesis algorithm (MOSAIC) for CNOT-based quantum circuits. Compared with the widely used search-based methods, MOSAIC is guaranteed to produce a result and can lead to a solution with much fewer steps. To evaluate the proposed algorithms, different circuits taken from the literature are used. The experimental results show the efficiency of the proposed algorithm.