In this paper, we propose a new anti-windup method with clear procedure of initialization to avoid overshoot in spite of saturation of control input. This method is based on a 2 degree of freedom model matching control system and by using a switch, instead of a control input and a reference output those are not affected by an input saturation, a saturated control input and an output are respectively used for updating a reference output and a feedforward input. By this means, when the input come to unsaturated, the Model Matching works correctly because the memorized values of the reference output utilized for updating reference output correspond with the past values of the output. Furthermore, a procedure to initialize the reference model with which the overshoots do not occur even if the control input is saturated is given. This method is suitable for systems in which overshoots are taboo such as tool machines and temperature controls. The proposed method is verified the effectiveness by numerical simulations and experiments.