In this paper, the monotonic convergence in the sense of sup-norm is studied. First, it is pointed out that, when typical iterative learning control (ILC) algorithms are applied to LTI systems, some huge overshoot in the sense of sup-norm may be observed even though monotonic convergence in the sense of lambda-norm is guaranteed. Then, new types of ILC algorithms are proposed for continuous-time systems and discrete-time systems to resolve such an undesirable phenomenon by adopting an intervalized learning scheme.