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Rough sets theory is often used for extracting if-then rules from categorical data sets with an objective function. In the conventional rough sets theory, the decision matrix method is known as one of the method extracting the rules. However, devising an efficient algorithm for the decision matrix method has seldom been reported to date. Consequently, this paper studies the process of reducing the decision matrix, finds several properties useful for the rule extraction, and proposes an effective algorithm for the extraction. The algorithm is implemented in a piece of software and a simulation experiment is conducted to compare the reduced time of the software base on the proposed algorithm with that of LEM2 software which is open to the public on the Internet, and is widely used throughout the world. As the results, the newly developed software is confirmed to perform exceptionally well under taxing conditions.