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This paper proposes an adaptive step-size method for blind source separation (BSS) suitable for robot audition systems. The design of the step-size parameter is a critical consideration when we apply BSS to real-world applications such as robot audition systems, because the surrounding environment dynamically changes in the real world. It is common to use a fixed step-size parameter that was obtained empirically. However, because of environmental changes and noise, the performance of BSS with a fixed step-size parameter deteriorates and the separation matrix sometimes diverges. Several adaptive step-size methods for BSS have been proposed. However, there are difficulties when applying them to robot audition systems for example, low-computational cost requirements, being free from manual parameter adjustment and so on. We propose an adaptive step-size method suitable for robot audition systems. The proposed method has the following merits: 1) low computational cost; 2) no parameters to be adjusted manually; and 3) no additional preprocessing requirements. We applied our method to six different BSS algorithms for an eight-channel microphone array embedded in Honda's ASIMO robot. The method improved the performance of all six algorithms in experiments on separation and recognition of simultaneous speech. Moreover, the method increased the amount of calculation by less than 10% compared with the original calculation used in most BSS algorithms.