On the puiseux theorem

In this article, based on the paper “Ha Huy Vui, Nguyen Hong Duc. On the Lojasiewicz exponent near the fibre of polynomial mappings, Ann. Polon. Math. 94 (2008), 43-52”, we give a different algorithm computing Newton - Puiseux roots of a complex polynomial in two variables. This algorithm is more effective in practice.