<p>We construct a new class of fully decoupled and higher-order implicit-explicit schemes for the Cahn–Hilliard–Navier–Stokes System, which is a phase-field model of two-phase incompressible flows, based on the generalized scalar auxiliary variable approach with the new relaxation for the Cahn–Hilliard equation and the consistent splitting method for the Navier–Stokes equations. These schemes are linear, fully decoupled, only require solving a sequence of elliptic equations with constant coefficients at each time step. We show that numerical solutions of these schemes are uniformly bounded without any restriction on time step size. Furthermore, we carry out a rigorous error analysis for the first-order scheme and establish optimal global-in-time error estimates for the phase function, velocity and pressure in two and three-dimensions. Several numerical examples are presented to validate the accuracy and robustness of the proposed schemes.</p>