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For the data which are mixed with an orthogonal system in the independent component analysis, that is the mixing matrix of the observation data is an orthogonal matrix, there is no an algorithm in this case at present except ones to the data with a general nonsingular mixing matrix. This paper presents an algorithm for this kind of the low order correlation data. The algorithm can be ensured in theory that the feasible solution of the problem with an orthogonal mixing matrix is the global optimal solution. Simulation experiments illustrate the efficiency of the algorithm.