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Let $\phi$ be a birational map of the complex projective plane. We know that$\phi$ can be written as a composition of automorphisms of$\mathbb{P}^2_\mathbb{C}$ and the standard quadratic birational map $\sigma$.This writing, that is non-unique, is minimal if the number $\mathfrak{n}(\phi)$of $\sigma$ is as small as possible. We prove that if $\phi$ is of degree$d\geq 2$, then $\big[\frac{\ln d}{\ln 2}\big]\leq\mathfrak{n}(\phi)\leq2(2d-1)$.

N\oe ther decomposition for birational maps