Summary: Nyberg and Knudsen proved that the maximum average of differential probability (ADP_{max}) and the maximum average of linear probability (ALP_{max}) of Feistel cipher with over 4 rounds can be evaluated as ADP_{max} 2DCP^{2}_{max} and ALP_{max} 2LCP^{2}_{max} using the maximum of defferential characteristic probability (DCP_{max}) and the maximum of linear characteristic probability (LCP_{max}) per round. This paper shows ADP_{max} DCP^{2}_{max} and ALP_{max} LCP^{2}_{max} if the F function is a bijection and the Feistel cipher has more than 3 rounds. The results prove that Feistel ciphers are stronger against differential and linear cryptanalyses than previously thought. Combining this result with that of Luby and Rackoff, the implication is that the 3-round Feistel cipher could be used as a building block cipher for the construction of provable secure block cipher algorithm.