Abstract: A concept of function matrix is put forward.With proving the isomorph between the function matrix algebra systems and the Boolean algebra’s disjunction-conjunction systems,a method of extending the function matrix is proposed,and the expanding theorem of the extended function matrix is proven.By expanding and reducing the extended function matrix step by step,a function-solving algorithm is presented and realized. Experimental results show that the algorithm effectively downsizes the solution space,improves function-solving efficiency and promotes innovation conflicts’detection and orientation in conceptual design.