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In this paper we show that we are close at the proof that the type of characteristics used by Biham and Shamir in their differential attack on DES [3] are in fact the best characteristics we can find for DES. Furthermore we show that the criteria for the construction of DES-like S-boxes proposed by Kim [6] are insufficient to assure resistance against differential attacks. We show several good iterative characteristics for these S-boxes to be used in differential attacks. Finally we examine the probabilities of the two characteristics used by Biham and Shamir in [3], We found that for some keys we do not get the probabilities used in the attack. We suggest the use of 5 characteristics instead of two in the attack on DES.