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Several methods have been suggested to detect influential observations in the linear regression model and a number of them have been extended for the multivariate regression model. In this article we consider the multivariate general linear model, Y = XB + ε, which contains the linear regression model and the multivariate regression model as particular cases. Assuming that the random disturbances are normally distributed, the BLUE of ΛB is also normally distributed. Since the distribution of the BLUE of ΛB and the distribution of the BLUE of ΛB in the model with the omission of a set of observations differ, to study the influence that a set of observations has on the BLUE of ΛB , we propose to measure the distance between both distributions. To do this we use Rao distance. [ABSTRACT FROM AUTHOR]