An unsupervised competitive learning algorithm based on the classical k-means clustering algorithm is proposed. The proposed learning algorithm called the centroid neural network (CNN) estimates centroids of the related cluster groups in training date. It is based on the observation that synaptic vectors converge to the centroids of clusters as learning proceeds in conventional unsupervised competitive learning algorithms such as SOM or DCL. The centroid, or conditional expectation, can minimize the mean-squared error of the vector quantization. As is the case with SOM or DCL, the synaptic vectors converge to the centroids of clusters as learning proceeds in CNN. However, the CNN finds locally optimal synaptic vectors for each datum presented and consequently converges to the centroids of clusters much faster than conventional algorithms. This centroid neural network can be used for generating the clusters using user data. The data may either image pixels or tables of information. One of the very advantageous features in the CNN algorithm is that the CNN does not require a schedule for learning coefficients. The CNN rather finds its optimal learning coefficient in each representation of data vectors. The CNN can also reward and punish by learning coefficients for winners and losers, respectively. Unlike SOM or DCL, the CNN also does not require the total number of iteration in advance.