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In the past few years, a lot of work has been done on simulating Boolean Circuits with biomolecular computation. In this paper, we present a new DNA-based evaluation algorithm for a Boolean circuit consists of NAND gates. This algorithm employs standard bio-molecular techniques. The contribution of this research is that the proposed model has been implemented using only three molecular operations. Furthermore, the number of passes in each level is decreased to less than half of existing models. Also the proposed implementation avoids the use of error-prone techniques such as PCR. These advantages have led to a faster, easier and more efficient algorithm. Time complexity of this algorithm is proportional to the depth of circuit.