The dispersion and volatility of transmission tariffs can provide an unsafe environment for generation investors in electrical systems, which are constantly growing. Dispersion and volatility occur, for example, in Brazil, where the Long Run Marginal Costs (LRMC) method is applied to calculate transmission tariffs. To solve this problem, this paper proposes a new Transmission Tariff Computation (TTC) approach based on the LRMC method and the min-max optimization technique. The proposed method uses the LRMC approach and the min-max optimization technique to seek less-dispersed transmission tariffs. The proposed modified LRMC method can be employed to optimize tariffs for generators and loads jointly or separately. This choice should be based on the network topology. The results are presented for a 6-bus and the IEEE 118-bus systems. The modified LRMC method is compared with the traditional LRMC method, currently in use in Brazil, and the classical Pro rata technique. Finally, some conclusions are presented.