We propose a simple O([n5/ log n]L) algorithm for linear programming feasibility, that can be consideredas a polynomial-time implementation of the relaxation method. Our work draws from Chubanov’s Divide-and-Conquer’’ algorithm (Chubanov, 2012), with the recursion replaced by a simple and more efficient iterative method. A similar approach was used in a more recent paper of Chubanov (2013)