Subspace clustering tries to find groups of similar objects from the given dataset such that the objects are projected on only a subset of the feature space. It finds meaningful clusters in all possible subspaces. However, when it comes to the quality of the resultant subspace clusters most of the subspace clusters are redundant. These redundant subspace clusters don’t provide new information. Hence there is a need for eliminating such redundant subspace clusters and output only those subspace clusters which are non redundant and each of them contributing some unique information to the data miner. The set of non redundant subspace clusters is helpful for easy analysis. In order to accomplish this, the concept of closedness has been applied to the subspace clusters. An algorithm known as Finding Closed Subspace Clusters (FCSC) is presented which efficiently outputs the closed subspace clusters from a given set of subspace clusters produced from any subspace clustering algorithm. Based on the experimental study conducted, the number of clusters generated by FCSC has been greatly reduced when compared to the existing SUBCLU algorithm and the average purity of the clusters is marginally improved without loss of coverage.