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Some issues on the Expectation-Maximisation process for Maximum Likelihood Linear Regression. VI Jornadas en Tecnología del Habla and II Iberian SLTech Workshop (FALA 2010), 2010.The Maximum Likelihood Linear Regression (MLLR) technique has commonly been used in speaker adaptation. In the computation of the transformation matrix usually only one iteration of the Expectation-Maximisation (EM) algorithm is used, but there is not a complete study about results with a different number of iterations. We analyze how the number of iterations affects to the adaptation. The obtained results lead us to suggest a new method to accelerate the convergence of adaptation. Additionally, we propose a way to verify the contribution of the different adaptation matrices obtained in the EM process. We present experiments with the Wall Street Journal corpus whose aim is to determine the best option for the MLLR technique with respect to the number of EM iterations and the quality of the new convergence criterion.