Abstract: To overcome the drawbacks of slow convergence speed and possible singular solutions of existing non-symmetrical joint diagonalization algorithm, we first present a least-squares criteria based non-symmetrical cost function for joint diagonalization, in which a penalty term is added to the classical least-squares criteria to avoid singular solutions. Then a non-symmetrical non-orthogonal fast joint diagonalization algorithm is developed by using a cyclic minimizer technique. The performance analysis shows that the present algorithm globally asymptotically converges to the stable stationary point and has the invariance property. The relation between left and right diagonalization matrices is also investigated to show that the non-symmetrical joint diagonalization is a more general form for joint diagonalization problem. The simulation results show that the proposed algorithm converges faster than the original algorithm, and that the interference to signal ratio (ISR) is also significantly improved.