Splitting schemes are a natural and easy to implement approach to integrate numerically in time differential equations. However, high order splitting methods suffer in general from an order reduction phenomena when applied to the integration of partial differential equations with non-periodic boundary conditions. In this talk, inspired by recent corrector techniques for the second order Strang splitting method, we present a new splitting method of order three for a class of semilinear parabolic problems that avoids order reduction. We prove the third order convergence of the method in a simplified linear setting and confirm the result by numerical experiments. Moreover, we observe numerically that the high order convergence persists for an order four variant of a splitting method, and also for a nonlinear source term.