In this article we revisit Newton's iteration as a method to find the G or R matrix in M/G/1-type and GI/M/1-type Markov chains. We start by reconsidering the method proposed in Ref.[ 15 Neuts , M.F. Moment formulas for the Markov renewal branching process . Advances in Applied Probability 1976 , 8 , 690 – 711 .[Crossref], [Web of Science ®] , [Google Scholar] ], which required O(m 6 + Nm 4) time per iteration, and show that it can be reduced to O(Nm 4), where m is the block size and N the number of blocks. Moreover, we show how this method is able to further reduce this time complexity to O(Nr 3 + Nm 2 r 2 + m 3 r) when A 0 has rank r < m. In addition, we consider the case where [A 1 A 2…A N ] is of rank r < m and propose a new Newton's iteration method which is proven to converge quadratically and that has a time complexity of O(Nm 3 + Nm 2 r 2 + mr 3) per iteration. The computational gains in all the cases are illustrated through numerical examples.