The problem of finding a feasible solution of a linear inequlity system arises in numerous contexts. González-Gutiérrez and Todorov have proposed an algorithm, called extended relaxation method, for solving the feasibility problem, and proved its convergence. Later on, they proved a linear rate of convergence for a class of extended relaxation methods depending on a parameter. In this paper, we shrink this class of extended relaxation methods to just one, generalizing the step iteration. We prove convergence and investigate the convergence rate. Numerical experiments have been performed, as well.