In this work, based on a Brin's article, we explain the structure of automorphism group of F, via a short exact sequence involving the subgroup of automorphisms of F together with the product of two copies of Thompson s group T. We will use a key theorem by McCleary and Rubin to realize each automorphism as conjugation by a homeomorphism in R. The previous short exact sequence will be obtained by just analyzing which shape these normalizing homeomorphisms must have. A crucial property of F, which we need to prove this theorem by McCleary and Rubin, and which we will use along all this work, is its k-transitivity on dyadic numbers for all k.