A new Cooperative Learning Control problem is introduced where a dynamical system is controlled by the sum of two controllers. Each of the two controllers, we design, has the structure of an iterative learning controller, which learns to track a desired, a priori chosen, output sequence. Once learned, the strength of one of the controller is reduced while this loss of control is iteratively transfered to the other controller. There is no direct communication between the two controllers and each controller updates iteratively, using the error signal between the system and the desired output. The point of this paper is to show that 'controller participation' can be iteratively transferred until one controller has completely acquired full control of the closed loop system. An important application of the proposed cooperative control system is in Rehabilitation of stroke patients, wherein a loss of control in the arm movement is initially aided by additive control signals from a computer. Subsequently, with therapeutic recovery, dependence on the computer control is reduced while the patient learns to be self reliant on his/her own motor control capability. The proposed cooperative control is illustrated using a non-square linear dynamical system in discrete time and we also consider a 2-link arm as an additional example of a nonlinear system.