In this paper, a new approach that is based on EEAC & only with network solutions for CS&S in the transient stability assessment is developed. The proposed CS&S algorithm in conjunction with EEAC to include the capability of performing on-line TSA without TDS is used to calculate the critical clearing time for stability index. In this algorithm, all generators are represented by classical models and all loads are represented by constant impedance load models. The accelerating & synchronizing power coefficient as an index is determined at its disturbance through solving network equation directly. As mentioned above, a new index for generator is generally used to determine the critical generators group. The generator rotor angle is fixed for non-critical generators group, but has equal angle increments for critical generators group. Finally, the critical clearing time is calculated from the power-angle relationship of equivalent OMIB system. The proposed CS&S algorithm currently being implemented is applied to the KEPCO system. The CS&S result was remarkably similar to TSAT program and SIME. Therefore, it was found to be suitable for a fast & highly efficient CS&S algorithm in TSA. The time of CS&S for the 139 contingencies using proposed CS&S algorithm takes less than 3 seconds on Pentium 4, 3GHz Desktop.