We discuss some undesirable phenomena associated with the lambda-norm that is used in the proof of convergence of the iterative learning controller (ILC). Specifically, we first report that huge overshoot may be observed in the output trajectory error, even though the applied learning algorithm has been proved to be exponentially convergent with respect to the lambda-norm. This is because of the way in which the lambda-norm converges differs from that of the sup norm. We then investigate the relation between the lambda-norm and the sup norm. Finally, we present a simple method to remedy the undesirable feature of the conventional ILC.