This paper presents a Robust Fisher Linear Discriminant (FLD) Model (RFM) for dimensionality reduction. The theoretical and experimental studies show that the RFM improves the FLD by (i) the robust estimate based on the probabilistic learning technique (ii) the stable computation procedure via diagonalizing two symmetric matrices. The experiments show the clear improvements when using the RFM instead of FLD. In particular, the RFM method increases the recognition rate by 20%-40% compared to the FLD in the small sample problem such as face recognition, and achieves a better and more stable accuracy when dealing with the heteroscedastic data such as handwriting images. We also expect that the result reported in this paper will impact diverse areas of research.