A synthetic jet actuator with double nozzles is developed to control the leeward vortices behind the slender body at a high angle of attack. Periodic alternating disturbance at the nose tip of the slender body is continuously provided by the alternating synthetic jets. A series of experiments is conducted in a low speed and low turbulence wind tunnel. The results show that the alternating synthetic jets at the nose tip can achieve a suitable control effect in which the lateral force is eliminated. For a very high angle of attack, the leeward vortices behind the slender body are in the inherently bi-stable state; in this state, the symmetric distribution formation by the leeward vortices is nearly impossible. However, the alternating disturbance of the nose tip can break the bi-stable state and transform it into other two states, which are the unsteady switched state of the leeward vortices and the quasi-steady symmetric state. Varying the control frequency significantly affects the state of the leeward vortex. In the range of the lower control frequency, the leeward vortices switch back and forth and follow the cycle of the alternating disturbance at the nose tip. In the range of the higher control frequency, the leeward vortices are in a stable symmetric distribution state. As the alternating disturbance frequency increases from lower to higher, the switched amplitude of the leeward vortices decreases and the unsteady switched state of the leeward vortices gradually changes to the quasi-steady symmetric state. This amplitude reduction occurs because the position of the leeward vortices is very sensitive to the alternating disturbance of the nose tip and is related to the inertia effect of the fluid.