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Classification methods have been widely applied in most brain computer interfaces (BCIs) that control devices for better quality of life. Most existing classification methods for P300-based BCIs extract features based on temporal structure related to P300 components of event-related potentials (ERPs). Some others exploit the spatial distribution of ERPs optimally selected by recursive channel elimination. However, none of them employed multilinear structures which exploit hidden features in P300-based BCI data. In this paper, we propose a new feature extraction method based on tensor decomposition for ERP-based BCIs. The method seeks an optimal feature subspace simultaneously spanned by temporal and spatial bases, and additional bases which indicate a variant of ERPs obtained by different degrees of polynomial fittings. The proposed method has been evaluated by both the BCI competition III data set II and the affective face driven paradigm data set, and achieved 92% and 95% classification accuracies respectively, which were better than those of most existing P300-based BCI algorithms.