Metric learning is one of the fundamental problems in person re-identification. However, a good number of the current techniques do not generalize well in the presence of outliers. Toward this, we present a robust discriminative subspace learning technique in this letter. We learn the subspace by maximizing the ratio of between class covariance and within class covariance using L1 norm instead of the conventional L2 norm. We theoretically show the iterative approach of computing the subspace. In case of noisy data, our experimental results demonstrate an overall average improvement of more than 4.2% in Rank-1 accuracy on CUHK03, Market1501, and DukeMTMC4ReID compared to popular metric learning algorithms.