Direct methods were developed to reduce computation time of transient stability assessment. Each method has its advantage and its own algorithm, which raises some differences between them. A new method was developed for providing the mathematical proof for the RAte of Change of Kinetic Energy (RACKE) method, yet become another direct method to compete with others. It was abbreviated (IRACKE) or Improved RACKE. A test power system was implemented to demonstrate the advantage of IRACKE over RACKE, the step-by-step, and the eminent Lyapunov direct method using three different energy functions found in the literature. This paper provides a comparison between the above methods and proves the superiority of IRACKE over others.