Abstract
Finta [2], recently proposed a complex version of iteration procedures for holomorphic functions. The general theorem of the complex iteration function has developed by using the complex mean value theorem and discussed several iterative procedures for holomorphic functions. In this paper, we redevelop the general theorem of the complex iteration function by applying the fundamental theorem of the complex line integral. It is shown that all the results derived in the paper of Finta have been improved by the results of this paper.