In this paper, we develop a new unsupervised learning clustering neural network method for clustering problems in general and for solving machine-part group formation problems in particular. We show that our new approach solves a very challenging problem in the area of machine-part group formation. A review of machine-part group formation methods and unsupervised learning artificial neural network methods is given. We modify the well-known competitive learning algorithm by using the generalized Euclidean distance, and a momentum term in the weight vector updating equations. The cluster structure can be adjusted by changing the coefficients in the generalized Euclidean distance. The algorithm is flexible and applicable to many practical problems. We also develop a neural network clustering system which can be used to cluster a 0-1 matrix into diagonal blocks. The developed neural network clustering system is independent of the initial matrix and gives clear final clustering results which specify the machines and parts in each group. We use the developed neural network clustering system to solve several machine-part group formation problems, in which the machine-part incidence matrix is to be clustered into a diagonal block structure. An algorithm is developed to consider lower and upper bounds on the number of machines for each cell. The computational results are compared with those from the well-known rank order clustering and directive clustering analysis methods.