Abstract: Considering the features of analytic functions, the properties of poles and essential singularity in solitary singularities of the complex functions are discussed. A new method for finding the poles, orders, and the essential singularity of complex functions is obtained and put into application. Practice shows that the new solution is more convenient and efficient than the original method, which saves a lot of work and is worthy of promotion.

Key words: complex function, pole, essential singularity, new method