We give a new proof of multisummability of formal power series solutions of a non linear meromorphic differential equation. We use the recent Malgrange-Ramis definition of multisummability. The first proof of the main result is due to B. Braaksma. Our method of proof is very different: Braaksma used Écalle definition of multisummability and Laplace transform. Starting from a preliminary normal form of the differential equation$$x\frac{d\overrightarrow{y}}{dx}={\overrightarrow{G}}_{0}\left(x\right)+\left[\lambda \left(x\right)+{A}_{0}\right]\overrightarrow{y}+{x}^{\mu}\overrightarrow{G}(x,\overrightarrow{y}),$$the idea of our proof is to interpret a formal power series solution...