In this paper, we implement the factor model for deriving the covariance matrix that is used for a Mahalanobis distance. The distributional properties of the new Mahalanobis distances are derived. A general case on contamination effects ofoutliers on Mahalanobis distances from separate parts of the factor model are also investigated. An empirical example indicates the difference between the new proposed separated Mahalanobis distances and the original Mahalanobis distance.