This paper presents a new method to design non-parallel distributed compensation (non-PDC) laws for Takagi- Sugeno fuzzy systems with local nonlinear models subject to actuator saturation. Based on specific congruence transformations, the local stabilization conditions are derived using Lyapunov stability theorem. The local design framework is established through an effective treatment of the sector-bound conditions for the input-saturation phenomenon and the nonlinearities in the consequents of the fuzzy systems. Using a non-quadratic Lyapunov function candidate, the control design is reformulated as an LMI-based optimization problem with a line search over a parameter, which can be effectively solved with convex optimization techniques. In particular, we theoretically prove that the new control method is less conservative compared to that derived from a standard non-PDC controller. Illustrative examples are provided to point out the interests of the proposed control method.