In this paper, we proposed Fittest Individual Refinement (FIR), a crossover based local search method for Differential Evolution (DE). The FIR scheme accelerates DE by enhancing its search capability through exploration of the neighborhood of the best solution in successive generations. The proposed memetic version of DE (augmented by FIR) is expected to obtain an acceptable solution with a lower number of evaluations particularly for higher dimensional functions. Using two different implementations DEfirDE and DEfirSPX we showed that proposed FIR increases the convergence velocity of DE for well known benchmark functions as well as improves the robustness of DE against variation of population. Experiments using multimodal landscape generator showed our proposed algorithms consistently outperformed their parent algorithms. A performance comparison with reported results of well known real coded memetic algorithms is also presented.