Using the semi-tensor product method, this paper investigates the Boolean derivative calculation with application to fault detection of combinational circuits, and presents a number of new results. First, a new set of formulas is obtained to calculate the Boolean derivative by the semi-tensor product method. Then, the obtained new results are applied to detecting the multiple faults of combinational circuits, and a new detection method is proposed. Finally, two illustrative examples are studied by using the results obtained in this paper. The study of illustrative examples shows that the new detection method can be used for detection of more than two faults effectively. (C) 2012 Elsevier Ltd. All rights reserved.