We propose an original scheme for the time discretization of a triphasic Cahn- Hilliard/Navier-Stokes model. This scheme allows an uncoupled resolution of the discrete Cahn-Hilliard and Navier-Stokes system, is unconditionally stable and preserves, at the discrete level, the main properties of the continuous model. The existence of discrete solutions is proved and a convergence study is performed in the case where the densities of the three phases are the same.