A number of tests for univariate normality exist in the literature having been proposed by various authors from time-to-time. Among those many, the procedure of Shapiro and Wilk (1965) is generally considered an omnibus test owing to its powerful performance in detecting departures from normality. Recently, a few multivariate generalizations of this test have been introduced, including one by Alva and Estrada (2009) and another by Sakthivel and William (2015). In this paper, another simplified generalization of Shapiro-Wilk test is considered. The critical values of the proposed statistic obtained by drawing simulated samples from multivariate normal distribution for dimensions 2 and 5 are given. The power of the proposed test is compared to the power of the tests referred above for a choice of entirely non-normal alternatives. Software for the same is developed in R Language.