In this paper, we propose a robust and efficient algorithm for generalized orthonormal discriminant vectors (GODV). The major advantage of the proposed method is the use of the rank-one update technique, rather than the Lagrange multipliers method, to iteratively derive the formula of computing the discriminant vectors of GODV. By contrast with the previous algorithms of GODV, the proposed algorithm has the computational efficiency and the numerical stability because of the avoidance of solving the inverse computation of matrices. Moreover, the proposed algorithm can be easily extended to tackle the nonlinear problem via kernel trick. The performance of the proposed algorithm is tested on the Yale face database and ORL face database, respectively.