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This paper proposes a new iterative learning control scheme to efficiently construct the control law for discrete time systems. Different from the typical algorithms of iterative learning control in the construction of control law, the new iterative learning controller is presented by using the geometric vector rotation. New parameters with clear geometric meanings are employed here and the structure of the algorithm is more convenient for adjusting the controllers in engineering practice. Furthermore, a detailed convergence analysis of the algorithm is given, and it is theoretically proven that the proposed algorithm ensures that the resulting closed loop system is stable and the tracking error converges to zero exponentially. The result of the simulations given demonstrates the effectiveness of the new geometric algorithm. [ABSTRACT FROM AUTHOR]