Abstract: Updating equations for linear models have been investigated for several years, however they have been restricted to the models with uncorrelated error structure, or considered for univariate linear models involving fixed parameters. This paper has considered updating equations for multivariate linear models with correlated error structure, and outlined updating equations of BLUE of unknown parameter matrix and residual when parameter, data or index is supplemented. The formulae are fitted for the cases of both fixed and random parameter matrices.