Let f be a (germ of ) holomorphic self-map of ℂ² such that the origin is an isolated fixed point and such that df_O=id. Let v(f) be the degree of the first nonvanishing term in the homogeneous expansion of f−id. We generalize to ℂ² the classical Leau-Fatou flower theorem proving that there exist v(f)−1 holomorphic curves f-invariant, with the origin in their boundary, and attracted by O under the action of f.