This paper presents a numerical simulation of statistically stationary two-dimensional turbulence. Navier−Stokes equations are integrated in an adaptive wavelet basis where only the evolution of significant coefficients is computed. The forcing of the flow is also done in wavelet space with enstrophy being injected in both space and scale. The results show that the flow has reached a statistically stationary state, which is proved by the fact that energy and enstrophy remain constant during the flow evolution while the energy spectrum and the PDF of vorticity are also maintained. This new forcing, defined in wavelet space, allows to model the local production of vortices by instabilities as generically observed in turbulent shear flows.