We propose a method to find the community structure in complex networks based on an extremal optimization of the value of modularity. The method outperforms the optimal modularity found by the existing algorithms in the literature giving a better understanding of the community structure. We present the results of the algorithm for computer-simulated and real networks and compare them with other approaches. The efficiency and accuracy of the method make it feasible to be used for the accurate identification of community structure in large complex networks.