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This article analyzes the drawbacks of linear programming methods to solve the directional over-current relay coordination problem. The solution infeasibility of these methods is due to selectivity constraints, which reduce the upper bound of the time multiplier setting of some relays. This infeasibility can be avoided by making the upper bound of the time multiplier setting insensible to selectivity constraints. With the proposed algorithm based on this idea, the constraints causing infeasibility are identified in order to change their position in relation to possible solution areas. This change is achieved by increasing the relay pickup currents. The proposed algorithm is tested and evaluated on the IEEE 14-bus and 30-bus networks. The results show that the previously infeasible solution of linear programming becomes feasible with high efficiency.