Fujishige et al. (2009) [2] proposed an LP-Newton type algorithm specifically designed to solve linear programming problems (LPs) by repeatedly applying Wolfe’s algorithm. This approach involves iterative projections onto a particular case of a convex hull, represented as a zonotope, leveraging Wolfe’s algorithm to systematically resolve the LP. The computational complexity of the LP-Newton type algorithm remains unknown, while Wolfe’s algorithm is known to have exponential complexityqueryPlease check and confirm if the authors Given and Family names have been correctly identified.. In this paper, we introduce an alternative algorithm that solves the same class of LPs without relying on Wolfe’s algorithm. Our algorithm shares a key characteristic with the LP-Newton method, ensuring that it terminates after a finite number of iterations.