Rank metric code-based cryptography exists for several years. The security of many cryptosystems is based on the difficulty of decoding a random code. Any improvement in the complexity of the best decoding algorithms can have a big impact on the security of these schemes. In this article, we present an improvement on the recent GRS algorithm [1] and we obtain a complexity of O ((n − k)^ 3 m^3 q^( w (k+1)m/ n −m ))for decoding an error of weight w in an [n, k] F 2 m-linear code.