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This paper presents a preliminary study on a new vibrotactile rendering method which can make smoother directional vibrotactile flows on a thin plate. Both by actuating two piezoelectric actuators sequentially from one side to the opposite side and by controlling amplitude-modulated input excitation frequency from zero to the 1st mode of the resonant frequency of a thin plate, a user can feel a smoother directional vibrotactile flows on his/her palm as he/she touches the surface of the thin plate. Experimental results and a user study show that the proposed vibrotactile flow is smoother than the vibrotactile flow that can be generated by the traditional apparent tactile movement and phantom sensation generation methods. The smooth directional vibrotactile flow may be useful for identifying callers or give directional information in navigation maps in mobile devices.