The evolution of fingers in a double-diffusive system is investigated using numerical integration of two-dimensional equations of motion for an incompressible, Boussinesq fluid. The computational domain is periodic in the horizontal direction and is closed with no-flux boundary conditions in the vertical direction. The main result of this study is the evolution of the system from initially linear profiles for both fast and slow diffusing components to a layered state characterized by a finger zone sandwiched between two mixed layers. The horizontal boundaries in this system play an important role in the development of the layered state. At the top and bottom boundaries, light and heavy finger fluxes accumulate leading to the formation of mixed layers exhibiting larger-scale eddies. In the quasi-equilibrium state, the finger zone is characterized by broken wiggly fingers which do not extend across the entire interface. The salinity flux at the mid-depth of the domain is approximately proportional to the 4/3 power of the salinity difference between the mixed layers, except for the initial phase and for the run-down phase.