Modelling　the　covariance　structure　of　multivariate　longitudinal　data　is　more　challenging　than　its　univariate　counterpart,　owing　to　the　complex　correlated　structure　among　multiple　responses.　Furthermore,　there　are　little　methods　focusing　on　the　robustness　of　estimating　the　corresponding　correlation　matrix.　In　this　paper,　we　propose　an　alternative　Cholesky　block　decomposition　(ACBD)　for　the　covariance　matrix　of　multivariate　longitudinal　data.　The　new　unconstrained　parameterization　is　capable　to　automatically　eliminate　the　positive　definiteness　constraint　of　the　covariance　matrix　and　robustly　estimate　the　correlation　matrix　with　respect　to　the　model　misspecifications　of　the　nested　prediction　error　covariance　matrices.　The　entries　of　the　new　decomposition　are　modelled　by　regression　models,　and　the　maximum　likelihood　estimators　of　the　regression　parameters　in　joint　mean-covariance　models　are　computed　by　a　quasi-Fisher　iterative　algorithm.　The　resulting　estimators　are　shown　to　be　consistent　and　asymptotically　normal.　Simulations　and　real　data　analysis　illustrate　that　the　new　method　performs　well.