Abstract : Multilinear techniques are increasingly used in Signal Processing and Factor Analysis. In particular, it is often of interest to transform a tensor into another that is as diagonal as possible or to simultaneously transform a set matrices into a set of matrices that are close to diagonal. In this paper we propose a parameterization of the general linear group. Based on this parameterization Jacobi-type procedures for congruent diagonalization and multilinear decomposition problems are developed. Comparisons with an existing congruent diagonalization algorithm is reported.