The SWM4-DP polarizable water model [G. Lamoureux, A.D. MacKerell, Jr., B. Roux, J. Chem. Phys. 119 (2003) 5185], based on classical Drude oscillators, is re-optimized for negatively charged Drude particles. The new model, called SWM4-NDP, will be incorporated into a polarizable biomolecular force field currently in development. It is calibrated to reproduce important properties of the neat liquid at room temperature and pressure: vaporization enthalpy, density, static dielectric constant and self-diffusion constant. In this Letter, we also show that it yields the correct liquid shear viscosity and free energy of hydration.