Gaussian mixture models (GMM) have been widely and suc- cessfully used in speaker recognition during the last decades. They are generally trained using the generative criterion of maximum likelihood estimation. In an earlier work, we proposed an algorithm for discrimi- native training of GMM with diagonal covariances under a large margin criterion. In this paper, we present a new version of this algorithm which has the major advantage of being computationally highly e cient, thus well suited to handle large scale databases. We evaluate our fast algo- rithm in a Symmetrical Factor Analysis compensation scheme. We carry out a full NIST speaker identi cation task using NIST-SRE'2006 data. The results show that our system outperforms the traditional discrimina- tive approach of SVM-GMM supervectors. A 3.5% speaker identi cation rate improvement is achieved.