Reduced bio-basis is the minimal set of fixed-length sub-sequences of a biological sequence with maximum information. Sequence data are not numerical so centroid-based clustering algorithms are not directly applicable. The main contribution of this paper is to show how to apply centroid-based algorithms on biological sequences. The average similarity between a subsequence and other sub-sequences in a cluster is reduced to a similarity between the sub-sequence and an artificial centre formed in a similar way to the formation of the centre of symbolic objects. After applying the hard version of the proposed symbolic clustering algorithm, a possibilistic membership is computed for each sub-sequence that adds high outliers' rejection capability to the algorithm. Well-studied issues for the centroid-based approach such as parallelism or scalability can be applied to the proposed approach. Experimental results on several real datasets show that the proposed approach, in several respects, is superior to traditional methods.