In this paper, a discrete-frequency technique is developed for analyzing sufficiency and necessity of monotone convergence of a proportional higher-order-derivative iterative learning control scheme for a class of linear time-invariant systems with higher-order relative degree. The technique composes of two steps. The first step is to expand the iterative control signals, its driven outputs and the relevant signals as complex-form Fourier series and then to deduce the properties of the Fourier coefficients. The second step is to analyze the sufficiency and necessity of monotone convergence of the proposed proportional higher-order-derivative iterative learning control scheme by assessing the tracking errors in the forms of Paserval’s energy modes. Numerical simulations are illustrated to exhibit the validity and the effectiveness.