In this paper, the problem of system identification in H-infinity with general orthonormal basis functions is investigated. A two-stage algorithm is show to be robust, provided that the umber of basis elements as a function of the amount of data does not increase faster than O (N (2/5)). Worst-case identification error bounds in the H-infinity norm are derived. The algorithm also works on nonuniformly spaced frequency response measurements. An example is provided to illustrate the application of the algorithm.