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The flow behind a three-dimensional rotationally oscillating circular cylinder was studied by a numerical method. The computations were performed at a Reynolds number of 260, which is at a level that the flow wake has developed into a three-dimensional state called Mode-B. The purpose of this paper is to examine the influence of various rotational amplitudes (0.1-0.7) on the wake instability of the flow, while the oscillation frequency is fixed to the value of that measured in the wake of a stationary cylinder. The results show that the rotation with sufficiently high amplitude brings the flow back to its nominal two-dimensional state. Moreover, it is found that the value of the time-averaged drag and the RMS value of the lift are larger than those of a stationary circular cylinder.