Multivariate　longitudinal　data　is　often　encountered　in　the　jobs　of　statisticians　and　practitioners.　It　is　challenging　to　model　the　covariance　matrix　due　to　the　complex　structure　of　correlations　among　multiple　responses.　For　this　modeling　task,　several　effective　Cholesky　decomposition　based　methods　have　been　studied.　However,　direct　interpretation　of　the　covariation　structure　among　multiple　responses　is　still　less　well　investigated　to　the　best　of　our　knowledge.　In　this　paper,　we　propose　a　joint　mean-variance　correlation　modeling　method　based　on　the　triangular　angles　parameterization　(TAP)　for　the　correlation　matrix　of　bivariate　longitudinal　data.　The　proposed　unconstrained　parameterization　is　able　to　automatically　eliminate　the　positive　definiteness　constraint　of　the　correlation　matrix　and　leads　to　the　aforementioned　direct　interpretation.　Furthermore,　the　variance　matrix　is　diagonal　rather　than　block-diagonal,　so　the　positive-definiteness　constraint　of　this　matrix　can　be　easily　satisfied.　The　entries　of　the　proposed　decomposition　are　modeled　by　regression　models,　and　the　maximum　likelihood　estimators　of　regression　parameters　are　obtained.　The　resulting　estimators　are　shown　to　be　consistent　and　asymptotically　normal.　Simulations　and　a　study　of　poplar　growth　illustrate　that　the　proposed　method　performs　well.