In this paper, a new paradigm of clustering is proposed, which is based on a new Binarization of Consensus Partition Matrix (Bi-CoPaM) technique. This method exploits the results of multiple clustering experiments over the same dataset to generate one fuzzy consensus partition. The proposed tunable techniques to binarize this partition reflect the biological reality in that it allows some genes to be assigned to multiple clusters and others not to be assigned at all. The proposed method has the ability to show the relative tightness of the clusters, to generate tight cluster or wide overlapping clusters, and to extract the special genes which bear the profiles of multiple clusters simultaneously. A synthetic periodic gene dataset is analysed by this method and the numerical results show that the method has been successful in showing different horizons in gene clustering.