MISTY is a data encryption algorithm recently proposed by M. Matsui from Mitsubishi Electric Corporation. This paper focuses on cryptographic roles of the transform used in the MISTY cipher. Our research reveals that when used for constructing pseudorandom permutations, the transform employed by the MISTY cipher is inferior to the transform in DES, though the former is superior to the latter in terms of strength against linear and differential attacks. More specifically, we show that a 3-round (4-round, respectively) concatenation of transforms used in the MISTY cipher is not a pseudorandom (super pseudorandom, respectively) permutation. For comparison, we note that with three (four, respectively) rounds, transforms used in DES yield a pseudorandom (super pseudorandom, respectively) permutation. Another contribution of this paper is to show that a 3-round concatenation of transforms used in (the preliminary version of) the MISTY cipher has an algebraic property, which may open a door for various cryptanalytic attacks.