Abstract.    In 1990 Rivest introduced the hash function MD4. Two years later RIPEMD, a European proposal, was designed as a stronger mode of MD4. In 1995 the author found an attack against two of three rounds of RIPEMD. As we show in the present note, the methods developed to attack RIPEMD can be modified and supplemented such that it is possible to break the full MD4, while previously only partial attacks were known. An implementation of our attack allows us to find collisions for MD4 in a few seconds on a PC. An example of a collision is given demonstrating that our attack is of practical relevance.