Vaudenay[12] proposed a new way of protecting block ciphers against classes of attacks, which was based on the notion of decorrelation. He also suggested two block cipher families COCONUT and PEANUT. Wagner[14] suggested a new differential-style attack called boomerang attack and cryptanalyzed COCONUT’98. Cheon[5] suggested a new block cipher DONUT which was made by two pairwise perfect decorrelation modules and is secure against boomerang attack. In this paper we suggest an attack called difference distribution attack on DONUT. We also suggest an improved DONUT which is secure against difference distribution attack.