This paper presents a new adaptive algorithm for frequency-domain identification. The algorithm is related to the rational orthogonal system (Takenaka-Malmquist system). This work is based on an adaptive decomposition algorithm previously proposed for decomposing the Hardy space functions, in which a greedy sequence is obtained according to the maximal selection criterion. We modify the algorithm through necessary changes for system identification. (C) 2012 Elsevier Ltd. All rights reserved.