We study a so-called non-local Cahn-Hilliard model obtained as a constrained Wasser-stein gradient flow of some Ginzburg-Landau energy. When compared to the more classical local degenerate Cahn-Hilliard model studied in [C. M. Elliott and H. Garcke, SIAM J. Math. Anal., 27(2):404–423, 1996], the non-local model appears to take advantage of a larger flexibility on the phase fluxes to dissipate faster the energy, as confirmed by numerical simulations. We prove the existence of a solution to non-local problem by proving the convergence of the JKO minimizing movement scheme.