In this study, a positioning stage which is actuated by four pneumatic cylinders and supported by four coil-type spring isolators is considered. In our past studies, the base plate jerk feedback (BPJFB) scheme was realized as a Master-Slave system that could synchronize the motion of stage (as a slave) with the motion of base plate (as a Master) against the vibration caused by the natural vibration of the base plate. However, the stage itself was slightly oscillatory due to the high gains set to the outer loop controller. This self-oscillation of the stage was misunderstood to be the natural vibration of the base plate. However, although the self-oscillation of stage was controlled by the BPJFB scheme, the related theory and some significant experimental results were not provided. Therefore, this paper focuses on the suppression of the self-oscillation of stage and the related theory. The experimental results obey the corresponding theory and demonstrate a newly recognized property of the BPJFB scheme, indicating the improvement of the positioning speed and stability.