A method is presented to partition a given set of data entries embedded in Euclidean space by recursively bisecting clusters into smaller ones. The initial set is subdivided into two subsets whose centroids are farthest from each other, and the process is repeated recursively on each subset. An approximate algorithm is proposed to solve the original integer programming problem which is NP-hard. Experimental evidence shows that the clustering method often outperforms a standard spectral clustering method, albeit at a slightly higher computational cost. The paper also discusses improvements of the standard K-means algorithm. Specifically, the clustering quality resulting from the K-means technique can be significantly enhanced by using the proposed algorithm for its initialization.