Since shape memory alloy (SMA) actuators can generate large force per unit weight, they are expected as one of the next generation actuators for aircraft. To keep a position of conventional control surfaces or morphing wings with SMA actuators, the SMA actuators must keep being heated, and the heating energy is not small. To save the energy, a new control method proposed for piezoelectric actuators utilizing hysteresis in deformation [Ikeda and Takahashi, Proc. SPIE 8689 (2013), 86890C] is applied to an antagonistic SMA system. By using the control method any position can be an equilibrium point within hysteresis of stress-strain diagrams. To confirm a feasibility of the control method, a fundamental experiment is performed. The SMA wires are heated by applying electric current to the wires. When a pulsed current is applied to the two SMA wires alternately, the equilibrium position changes between two positions alternately, and when a series of pulse whose amplitude increases gradually is applied to one SMA wire, the equilibrium position changes like a staircase. However, just after the pulse the position returns slightly, that is, overshoot takes place. To investigate such a behavior of the system, numerical simulation is also performed. The one-dimensional phase transformation model [Ikeda, Proc. SPIE 5757 (2005), 344-352] is used for a constitutive model of the SMA wires. The simulated result agrees with the experiment qualitatively, including the overshoot. By examining volume fraction of each phase, it is found that the overshoot is caused by that austenite phase transforms into stress-induced martensite phase during the cooling process after the pulse.