Abstract: The method of“limiting argument” is one of the two most commonly used methods for the calculation of a single-valued branch. Through constructing counter examples, the misuses of the method of“limiting argument are pointed out for the calculation of a single-valued branch. The conditions for the use of the method are defined thus to expand the applicable scope of the method of“limiting argument” so that the uniqueness of the computational result is guaranteed. Moreover, three new examples which can be solved by the method of“limiting argument” are presented.