The consistent splitting schemes for the Navier-Stokes equations decouple the computation of pressure and velocity. However, only the first-order version of the consistent splitting schemes is proven to be unconditionally stable for the time dependent Stokes equations. We construct a new class of consistent splitting schemes of orders two to four for Navier-Stokes equations based on Taylor expansions at time $t_{n+\beta}$ with $\beta \ge 1$. By choosing suitable $k$, we construct, for the first time, unconditionally stable and totally decoupled schemes of orders two to four for the velocity and pressure, and provide rigorous optimal error estimates.