Performance of iterative clustering algorithms depends highly on the choice of cluster centers in each step. In this paper we propose an effective algorithm to compute new cluster centers for each iterative step for K-means clustering. This algorithm is based on the optimization formulation of the problem and a novel iterative method. The cluster centers computed using this methodology are found to be very close to the desired cluster centers, for iterative clustering algorithms. The experimental results using the proposed algorithm with a group of randomly constructed data sets are very promising.