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Common spatial pattern (CSP) algorithm is a highly successful method for the motor imagery based brain-computer interfaces (BCIs) in the case of two task conditions. But low information transfer rate (ITR) is an intrinsic problem that binary BCIs face, and restricts their practical application. The most effective method to increase ITR is to extend two mental tasks to multiple tasks. This paper generalizes binary CSP algorithm to multiple task conditions by approximate joint diagonalization based on quadratic optimization. This algorithm is used to five data sets recorded during a BCI experiment consisting of three motor imagery tasks and is evaluated by diagonalization error, convergence speed and classification accuracy. Results demonstrate that the performance of the algorithm is satisfactory.