Iterative learning control approaches often suffer from poor extrapolability with respect to exogenous signals, including setpoint variations. The aim of this paper is to introduce rational basis functions in ILC. Such rational basis function have the potential to both increase performance and enhance extrapolability. The key caveat that is associated with these rational basis function lies in a significantly more complex optimization problem when compared to using polynomial basis functions. In this paper, a novel iterative optimization procedure is proposed that enables the use of rational basis functions in ILC. A simulation example confirms (1) the advantages of rational basis functions compared to pre-existing results, and (2) the efficacy of the proposed iterative algorithm.