For simple tree multivariate order restriction, this paper defines a closed convex set inside the order restricted cone, and develops an algorithm for matrix projections onto this set. For the mean matrix in one-way MANOVA, the order restricted MLE (RMLE) is the projection of MLE onto the order restricted cone. It is proposed to use the projection onto this subset of the cone as a pseudo RMLE due to the simplicity of the computation and its good properties. © 2023 Elsevier B.V.