This article reports the first application of parallel factor analysis to high-order instrumental data generated from Shpol'skii matrixes at liquid helium temperature. Third-order data arrays-consisting of excitation modulated wavelength time matrixes-are collected with the aid of a cryogenic fiber-optic probe, a tunable dye laser, and a multichannel system for phosphorescence detection. The multidimensional data formats are applied to the analysis of 2,3,7,8-tetrachloro-dibenzo-para-dioxin in water samples. The experimental procedure is rapid and environmentally friendly. Complete sample analysis is accomplished in less than 15 min with only 100 muL of organic solvent (n-heptane). The feasibility to directly determine parts-per-trillion concentration levels of the target compound is demonstrated with heavily contaminated samples of unknown composition. The limits of detection, estimated from calibrations based on the univariate method and parallel factor analysis, are 0.060 and 0.092 ng.mL(-1), respectively; both referred to a 100 mL water sample.