Genetic algorithms have been used as an optimization tool using evolutionary strategies. Genetic algorithms cover three basic steps for population refinement selection, cross-over and mutation. In normal Real-coded genetic algorithm (RGA), the population of real variables generated after population refinement operations, is used for the computation of the objective function. In this paper we have shown the effect made by mapping the refined population towards better solutions and thereby creating more biased search. The mapping used is non-uniform in nature and is the function of the position of the individual w.r.t. the best solution obtained so far in the algorithm, and hence the name Non-Uniform RGA or in short NRGA. Tests were performed on standard benchmark problems. The results were promising and should encourage further research in this dimension.