Rainbow is a fast asymmetric multivariate signature algorithm proposed by J. Ding and D. Schmidt in [5]. This paper presents a cryptanalysis of Rainbow which enables an attacker provided with the public key to recover an equivalent representation of the secret key, thus allowing her to efficiently forge a signature of any message. For the set of parameter values recommended by the authors of Rainbow in order to achieve a security level strictly higher than 280, the complexity of our attack is less than 271 operations. This is 240 times less than the complexity of the best known attack used by the authors to dimension their system.