This paper proposes a new control parametrization under the model predictive control (MPC) framework for constrained linear discrete-time systems with bounded disturbances. The proposed parametrization takes the form of a special piecewise affine disturbance feedback in an effort to reduce conservatism. It is a generalization of linear disturbance feedback parametrization, introduced in the recent literature. Numerical computations and stability properties of the resulting MPC problem using the proposed parametrization are discussed. When the disturbance set and the problem data satisfy mild assumptions, the associated finite-horizon optimization can be computed efficiently and exactly. The advantage of the proposed parametrization over linear disturbance feedback is illustrated via numerical examples.