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In direct methods, the use of the controlling unstable equilibrium point (cuep) method has been taken with great acceptance. The reason of this acceptance is that the CUEP method takes into consideration the fault-on trajectory. This means that for each fault-on trajectory there is a specific CUEP. In the other hand, since the closest unstable equilibrium point (closest UEP) is unique, the closest UEP method does not take into consideration the fault-on trajectory. It means that using CUEP method results in a less conservative transient stability assessment than using the closest UEP method. Because the CUEP method takes into consideration the fault-on trajectory, it is necessary to find it every time we need to make a stability assessment. In order to make a good stability assessment, finding the true CUEP has a great importance. This paper shows that under some circumstances the BCU method may not be able to find the true CUEP for a specific trajectory. Moreover, a methodology than can improve the capability of BCU Method to successfully find the CUEP is shown. Finally, several applications to electrical power systems are shown.