Most state-of-the-art speaker recognition systems are based on discriminative learning approaches. On the other hand, generative Gaussian mixture models (GMM) have been widely used in speaker recognition during the last decades. In an earlier work, we proposed an algorithm for discriminative training of GMM with diagonal covariances under a large margin criterion. In this paper, we propose an improvement of this algorithm which has the major advantage of being computationally highly efficient, thus well suited to handle large scale databases. We also develop a new strategy to detect and handle the outliers that occur in the training data. To evaluate the performances of our new algorithm, we carry out full NIST speaker identification and verification tasks using NIST-SRE'2006 data, in a Symmetrical Factor Analysis compensation scheme. The results show that our system significantly outperforms the traditional discriminative Support Vector Machines (SVM) based system of SVM-GMM supervectors, in the two speaker recognition tasks.