This paper focuses on the problem of detecting multiple leverage points and outliers in multivariate linear models. It is well known that the identification of these points is affected by masking and swamping effects. To identify them, Rousseeuw(1985) used robust estimators of MVE(Minimum Volume Ellipsoids), which have the breakdown point of 50% approximately. And Rousseeuw and van Zomeren(1990) suggested the robust distance based on MVE, however, of which the computation is extremely difficult when the number of observations n is large, In this study, we propose a new algorithm to reduce the computational difficulty of MVE. The proposed method is powerful in identifying multiple leverage points and outliers and also effective in reducing the computational difficulty of MVE.