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In this letter, it is revealed that there exits an approximate linear relation between the changes in input pump powers and the resulting changes in the pump-power integrals in multiwavelength pumped fiber Raman amplifiers (MW-FRAs). Based on this fact, a novel efficient optimal design method for gain-flattened MW-FRAs is proposed. First, the optimal integral pump spectrum is found by genetic algorithm. Then, the matrix denoting the linear many-to-many relation is calculated. By this matrix, the optimal input pump powers resulting in the optimal pump-power integrals can be easily calculated. The optimal pump spectrum is obtained without time consuming trial-error adjustments or many times numerical simulations. Compared to other existing optimal design methods, our method has a substantial improvement in the efficiency without any expense of accuracy.