Abstract: Truncated differential cryptanalysis is a variant of differential cryptanalysis. In order to evaluate the ability of a block cipher against the truncated differential cryptanalysis, it is needed to give out the upper bound of the probability of the truncated differential chain. Masayuki Kanda et al. propose a conjecture about the upper bound of the probability of the truncated differential when the S-boxes in block cipher are the combination of the inverse function and a bijective affine transformation in GF(256). This paper gives out an evaluation about the upper bound of the probability of the truncated differential by assuming the S-boxes as bijective S-boxes and Masayuki Kandas conjecture is the special case of the problem that the evaluation considers. In some cases, the upper bound given by the evaluation is approaching to the conjecture. This conclusion can serve to evaluate the upper bound probability of the truncated differential chain. The results provide further support for the provable security of a block cipher against the truncated differential cryptanalysis in theory.