In this work, a new method for adaptive control of plants with input saturation is presented. The new anti-windup scheme can be shown to result in bounded closed-loop states under certain conditions on the plant and the initial closed-loop states. As an improvement in comparison to existing methods in adaptive control, a new degree of freedom is introduced in the control scheme. It allows to improve the closed-loop response when actually encountering input saturation without changing the closed-loop performance for unconstrained inputs.<eng>