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One important source of performance degradation in BCIs is bias towards one of the mental classes. Recent literature has focused on the general problem of classification accuracy drop, identifying non-stationarity as the generating factor, thus leading to several classifier adaptation approaches suggested as of today. In this work, we explicitly focus on bias elimination, demonstrating that the problem has two separate components, one related to non-stationarity and another one attributed to the nature of the feature distributions and the assumptions made by the classification methods. We propose a cued recalibration protocol including a supervised adaptation method and a novel framework for unbiased classification with a modified, unbiased Linear Discriminant Analysis classifier. Preliminary results show that our protocol can assist the subject to achieve quickly accurate and unbiased control of the BCI.