The reinforcement learning algorithms have often been applied to social robots. However, most reinforcement learning algorithms were not optimized for the use of social robots, and consequently they may bore users. We proposed a new reinforcement learning method specialized for the social robot, the FRAC-Q-learning, that can avoid user boredom. The proposed algorithm consists of a forgetting process in addition to randomizing and categorizing processes. This study evaluated interest and boredom hardness scores of the FRAC-Q-learning by a comparison with the traditional Q-learning. The FRAC-Q-learning showed significantly higher trend of interest score, and indicated significantly harder to bore users compared to the traditional Q-learning. Therefore, the FRAC-Q-learning can contribute to develop a social robot that will not bore users. The proposed algorithm has a potential to apply for Web-based communication and educational systems. This paper presents the entire process, detailed implementation and a detailed evaluation method of the of the FRAC-Q-learning for the first time.