In this brief, a novel self-weighted orthogonal linear discriminant analysis (SOLDA) problem is proposed, and a self-weighted supervised discriminative feature selection (SSD-FS) method is derived by introducing sparsity-inducing regularization to the proposed SOLDA problem. By using the row-sparse projection, the proposed SSD-FS method is superior to multiple sparse feature selection approaches, which can overly suppress the nonzero rows such that the associated features are insufficient for selection. More specifically, the orthogonal constraint ensures the minimal number of selectable features for the proposed SSD-FS method. In addition, the proposed feature selection method is able to harness the discriminant power such that the discriminative features are selected. Consequently, the effectiveness of the proposed SSD-FS method is validated theoretically and experimentally.