Abstract: The Modified One-step M-estimator (MOM) is a highly efficient robust estimator for classifying multivariate data. Generally, robust estimators came into existence as a solution to the inability of classical Linear Discriminant Analysis (LDA) to perform optimally in the presence of outliers. Thus, to solve this shortcoming, the robust MOM estimator is integrated with a highly robust scale estimator, Qn, in the trimming criterion of MOM. This introduces a new robust approach termed RLDAMQ for handling outliers encountered in multivariate data. The results show the superiority of RLDAMQ over the classical LDA and previously existing robust method in literature in terms of misclassification error evaluated through simulated data.