Abstract: In blind source separation, the second-order and higher-order cumulant matrices of pre-whitened signals have the structure orthogonal joint diagonalization. In eigendecomposition theory, the real symmetry matrices with the same eigenvectors can simultaneous diagonalization. In this paper, a direct orthogonal joint diagonalization algorithm based on eigendecomposition of the cumulant matrices is proposed for blind source separation. In practical computation, we only need part of the cumulant matrices, so the storage and calculation will be greatly reduced. The numerical simulation results show that the performance of our algorithm close to the one of JADE, it is effective for blind source separation.