Today large majority of researchers have focused on the research on accurate pattern mining methods. Clustering techniques are most preferable methods for pattern mining even in case of huge and growing data. Most of the real-life data applicable to pattern mining are non-crisp by nature. This means data can't be clearly separable into disjoint clusters. Thus uncertainty based models like rough sets are most preferable for representation of data under such circumstances. With rough set approach, every cluster is a rough set and hence is represented by upper and lower approximations. The data objects belong to the upper approximation may or may not belong to clusters and data objects which belong to lower approximation definitely belong to clusters. Refined rough K-Means algorithm was proposed by Peters in-order to improve the rough K-Means clustering algorithm proposed by Lingras. In this paper, we propose an extension of the refined rough K-Means algorithm of Peters to the context of covers. Experimental analysis shows that the proposed algorithm is more efficient than the refined rough K-means algorithm.