In this paper an alternating trilinear decomposition (ATLD) algorithm that is an improvement of the traditional PARAFAC algorithm without any constraints is described as an alternative algorithm for decomposition of threeway data arrays. It is based on an alternating least squares principle and an improved iterative procedure that, in a real trilinear sense, uses the Moore-Penrose generalized inverse with singular value decomposition. Its performance is compared with that of the traditional PARAFAC algorithm by a series of Monte Carlo simulations with different noise levels. It was found that the ATLD algorithm has a capability to converge faster than the traditional PARAFAC algorithm. The ATLD-based second-order calibration retains the second-order advantage that calibration in the presence of unknown interferents can be performed to provide satisfactory concentration estimates. Both algorithms have been used for simultaneous determination of overlapped chlorinated aromatic hydrocarbons measured by means of a high-performance liquid chromatograph with a diode array detector.