The necessity of online dynamic security assessment is getting apparent under Electricity Market environments, as operation of power system is exposed to more various operating conditions. For on-line dynamic security assessment, fast transient stability analysis tool is required for contingency selection. The TEF(Transient Energy Function) method is a good candidate for this purpose. The clustering of critical generators is crucial for the precise and fast calculation of energy margin. In this paper, we propose a new method for fast decision of mode of instability by using stability indices and energy margin. The method is a new version of our previous paper.[1] Case studies are showing very promising results.