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This paper deals with a decomposition of a set of stationary random processes: . The decomposition has the form: , etc., where the components have the following properties: for a fixed , they are completely correlated in pairs; for a fixed , they are uncorrelated in pairs. Assuming the spectral matrix of the 's as known, the spectral description of the 's given by a lower triangular matrix, is determined. This is achieved by both an iterative and a direct method. In both methods regular and singular cases are considered.