Conventional out-of-step islanding device generally takes relative power angles achieving 360° as the indication of out-of-step condition although the risk of such judgment relied solely on a fixed threshold of angle difference in complex power systems has been pointed out. A new method for islanding control of complex power systems is proposed. The system is separated at the oscillation center upon identification of a dynamic saddle point（DSP） on the time-varying OMIB equivalent trajectory transformed from real-time measurements of wide-area power angle trajectories by using the complementary-cluster center-of-inertial（CCCOI） transformation. The proposed method strictly conforms to the instability detection mechanism of extended equal-area criterion（EEAC） quantitative analysis theory， and the effectiveness of the method is demonstrated by simulation results. In some cases， the new method is able to detect the out-of-step condition earlier than the conventional out-of-step islanding criterion.