Abstract: Many procedures are available in the literature on testing for univariate normality. Among them, the procedure of Shapiro and Wilk (1965) is a very effective test to detect departures from normality. The Shapiro-Wilk procedure has been extended to test multivariate normality recently by Alva and Estrada (2009). The present paper proposes another approach to extend the Shapiro-Wilk procedure for testing multivariate normality. A simulation study has been carried out to get the critical values of the proposed statistic in order to make it applicable to dimensions 2 and 5. Power comparison of the new approach to the one given by Alva and Estrada (2009) is presented for a contaminated alternatives. The software for the same is developed in R Language.