A multivariate linear regression model Y~N (βM',Σ) is considered where some of the rows in the coefficient matrix β are constrained by synchronized order restrictions. A test scheme is derived for the homogeneity of the coefficient matrix using the likelihood-ratio test procedure under the assumption that the coefficient matrix Σ is known. When Σ is unknown, a new ad-hoc test statistic TH(Y) is proposed by replacing the covariance matrix with its estimator, where H is a non-empty subset of the row-index space {1,2,...,p}.The properties of TH(Y) are studied and a theorem is also stated on the distribution of TH(Y) which eventually helps us to estimate p-values using the Monte-Carlo method by simulation.