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In this paper, a novel caudal fin for actuating a robotic fish is presented. The proposed caudal fin waves in a vertical direction with a specific spatial shape, which is determined by a so-called shape factor. For a specific shape factor, a traveling wave with a vertical phase difference is formed on a caudal fin during fin motion. It will be shown by the analysis that the maximum reaction torque at the joint of a caudal fin varies depending on the shape factors. Compared with a conventional plate type caudal fin, the proposed fin with a shape factor of 2π can eliminate the reaction torque perfectly, while keeping the propulsion force unchanged. The benefits of the proposed fin will be demonstrated by experiments.