Partitional clustering algorithms are the most widely used approach in clustering problems. However, how to evaluate the clustering performance of these algorithms remains unanswered due to the lack of an efficient measure for accurately representing the separation among partitioned clusters. In this paper, based on two most commonly used partitional clustering algorithms, c-means and fuzzy c-means, and their variants, we developed a new measure, called as dual center, to represent the separation among clusters. The new measure can efficiently represent the separation among various clusters. According to the defined measure, a new validity index is proposed for evaluating the clustering performance of partitional algorithms. Two groups of benchmark datasets with different characteristics were used to validate the effectiveness of the proposed validity index. Experimental results provide evidence that the proposed validity index outperforms some existing representative validity indexes in the two groups of typical and representative datasets.