A new method, alternating penalty trilinear decomposition (APTLD), is developed for the decomposition of three-way data arrays. By utilizing the alternating least squares principle and alternating penalty constraints to minimize three different alternating penalty errors simultaneously, the intrinsic profiles are found. The APTLD algorithm can avoid the two-factor degeneracy problem and relieve the slow convergence problem, which is difficult to handle for the traditional parallel factor analysis (PARAFAC) algorithm. It retains the second-order advantage of quantification for analytes of interest even in the presence of potentially unknown interferents. In additions, it is insensitive to the estimated component number, thus avoiding the difficulty of determining a correct component number for the model, which is intrinsic in the PARAFAC algorithm. The results of treating one simulated and one real excitation–emission spectral data set showed that the proposed algorithm performs well as long as the model dimensionality chosen is not less than the actual number of components. Furthermore, the performance of the APTLD algorithm sometimes surpasses that of the PARAFAC algorithm in the prediction of concentration profiles even if the component number chosen is the same as the actual number of underlying factors in real samples. Copyright © 2005 John Wiley & Sons, Ltd.