A novel algorithm, four-way self-weighted alternating normalized residue fitting (SWANRF), which is an extension of its three-way form, for the decomposition of quadrilinear data with new weight factors, was proposed and applied to the quantitative analysis of serotonin contents in plasma samples. It was observed that the third-order calibration could not only retain a "second-order advantage" and but also obtain other advantages. The introduction of a fourth mode can relieve the serious problem of collinearity, which seems to be one of the "third-order advantages". The proposed algorithm shows great potential as a promising alternative for the third-order calibration of a four-way data array by contrasting with four-way parallel factor analysis (four-way PARAFAC). Furthermore, both algorithms mentioned above were utilized to analyze the 5-hydroxytryptamine (serotonin) contents in plasma samples by obtaining four-way array (excitation-emission-pH-sample) data, and produced satisfactory results. The serotonin contents in plasma samples obtained by using four-way SWANRF and four-way PARAFAC were 0.324 ± 0.005 and 0.348 ± 0.006 nmol mL(-1), respectively.