In 1973, Arimoto proved the strong converse theorem for the discrete memoryless channels stating that when transmission rate R is above channel capacity C, the error probability of decoding goes to one as the block length n of code word tends to infinity. He proved the theorem by deriving the exponent function of error probability of correct decoding that is positive if and only if R>C. Subsequently, in 1979, Dueck and Körner determined the optimal exponent of correct decoding. Arimoto's bound has been said to be equal to the bound of Dueck and Körner. However its rigorous proof has not been presented so far. In this paper we give a rigorous proof of the equivalence of Arimoto's bound to that of Dueck and Körner.