Iterative learning control (ILC) approaches often exhibit poor extrapolation properties with respect to exogenous signals, such as setpoint variations. This brief introduces rational basis functions in ILC. Such rational basis functions have the potential to both increase performance and enhance the extrapolation properties. The key difficulty that is associated with these rational basis functions lies in a significantly more complex optimization problem when compared with using preexisting polynomial basis functions. In this brief, a new iterative optimization algorithm is proposed that enables the use of rational basis functions in ILC for single-input single-output systems. An experimental case study confirms the advantages of rational basis functions compared with preexisting results, as well as the effectiveness of the proposed iterative algorithm.