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In this paper, by using well-known Eddington–Finkelstein coordinates instead of Painlevè coordinates, we study the tunneling effect of black holes. As examples of special static black holes, we calculate the tunneling rates of Gibbon–Maeda black holes. The result obtained by adopting Eddington–Finkelstein coordinates is in agreement with the Parikh’s standard result, Γ∼exp (−2Im S), which adopts the Painlevè coordinates. In addition, we discuss carefully the condition that the coordinates system in which we study the tunneling process should satisfy. In our opinion, the terms of the tunneling effect are not as strict as ones in Parikh’s paper and could be softened properly. [ABSTRACT FROM AUTHOR]