This paper describes a new ultra-fast contingency screening algorithm for on-line TSA without time simulation. All machines are represented in a classical model and the stability index is defined as the ratio between acceleration power during a fault and deceleration power after clearing the fault. Critical clustering of machines is done based on the stability index, and the power-angle curve of the critical machines is drawn assuming that the angles of the critical machines increase uniformly, while those of the non-critical ones remain constant. Finally, the critical clearing time (CCT) is computed using the power-angle curve. The proposed algorithm is tested on the KEPCO system comprised of 900-bus and 230-machines. The CCT values computed with the screening algorithm are in good agreement with those computed using the detailed model and the SIME method. The computation time for screening about 270 contingencies is 17 seconds with 1.2 GHz PC.