An outlier is an observation that appears to deviate from other observations in the sample and outlier detection is one of the most important tasks in data analysis. One of the fundamental assumptions of most parametric multivariate techniques is multivariate normality, which implies the absence of multivariate outliers. The basis for multivariate outlier detection is based on the Mahalanobis distance and outlier detection methods have been suggested for numerous applications in the literature. In this work, Tietjen-Moore test is generalized for multivariate data. A simulation study is carried out to evaluate the performance of the multivariate outlier detection methods under various conditions. The results show that the proposed method gives better results depending on whether or not the data set is multivariate normal.