Abstract: The algorithm, proposed for the computation of overdetermmed linear system with minimized L_∞-morn of the residual vector, is a direct descent method which minimizes the function in finite number of steps and is similar to that used in our algorithm for L_∞-problem. The algorithm, simple and convenient, is closely related to the active set method for solving linear programming. Finally the performance of the algorithm is demonstrated by solving a number of numerical examples on the IBM-PC micro-computer.