TRIZ solves difficult problems by finding contradictions in the problem itself. In TRIZ, a technical contradiction occurs when one function of a system is enhanced, the other function is deteriorated at the same time, and vice versa. On the other hand, a physical contradiction appears when two opposite properties are required from the same part of a system. Among TRIZ components, the ARIZ, algorithm for inventive problem solving, has developed by Altshuller for reducing trial-and-error while solving problems. It transforms difficult technical contradictions of a given problem into the corresponding physical contradiction to solve the problem easily. However, ARIZ-85c, the most recent version of the ARIZ, still has the brute-force feature inside. In this paper, we propose the Butterfly algorithm based on the Butterfly diagram to reduce the brute-force feature by giving the right direction when selecting technical contradictions and physical contradictions.