Multivariate　isotonic　regression　theory　plays　a　key　role　in　the　field　of　statistical　inference　under　order　restriction　for　vector　valued　parameters.　Two　cases　of　estimating　multivariate　normal　means　under　order　restricted　set　are　considered.　One　case　is　that　covariance　matrices　are　known,　the　other　one　is　that　covariance　matrices　are　unknown　but　are　restricted　by　partial　order.　This　paper　shows　that　when　covariance　matrices　are　known,　the　estimator　given　by　this　paper　always　dominates　unrestricted　maximum　likelihood　estimator　uniformly,　and　when　covariance　matrices　are　unknown,　the　plug-in　estimator　dominates　unrestricted　maximum　likelihood　estimator　under　the　order　restricted　set　of　covariance　matrices.　The　isotonic　regression　estimators　in　this　paper　are　the　generalizations　of　plug-in　estimators　in　unitary　case.　Crown　Copyright　(C)　2009　Published　by　Elsevier　Inc.　All　rights　reserved.