For the first time, a simple and environmentally friendly third-order/four-way calibration was applied for the simultaneous determination of five heavy-polycyclic aromatic hydrocarbons (PAHs) in interfering environments. The kinetic evolution of the Fenton degradation of benzo[a]pyrene, dibenz[a,h]anthracene, benzo[b]fluoranthene, benzo[k]fluoranthene and benz[a]anthracene was followed by recording full excitation-emission fluorescence matrices (EEFMs) of the samples at different reaction times, obtaining third-order EEFM-kinetic (EEFM-K) data. The sensitivity of the method was increased by carrying out the reaction in the presence of methyl-β-cyclodextrin. The four-way parallel factor (PARAFAC) algorithm, which was used for data processing, exploits the second-order advantage, allowing analyte concentrations to be estimated even in the presence of an uncalibrated fluorescent background. The clear superiority of the applied approach in comparison with second-order/three-way calibration performed with unreacting EEFMs is demonstrated, using two sets of samples with foreign compounds with particular spectral profiles. In one of the latter sets, the existence of a third-order advantage was explored and discussed. The feasibility to directly determine parts-per-trillion concentration levels of PAHs after a very simple solid-phase extraction with C18 membranes is established with natural water samples containing uncalibrated constituents.Fil: Carabajal, Maira Daniela. Universidad Nacional de Rosario. Facultad de Ciencias Bioquímicas y Farmacéuticas. Instituto de Química Rosario (IQUIR-CONICET); Argentina.Fil: Arancibia, Juan Alberto. Universidad Nacional de Rosario. Facultad de Ciencias Bioquímicas y Farmacéuticas. Instituto de Química Rosario (IQUIR-CONICET); Argentina.Fil: Escandar, Graciela Mónica. Universidad Nacional de Rosario. Facultad de Ciencias Bioquímicas y Farmacéuticas. Instituto de Química Rosario (IQUIR-CONICET); Argentina.