Abstract The use of principal components to reduce the number of dimensions so that graphieal representation of the data is possible has been developed. One. of the most important applications is the connexion with cluster analysis. It has not been defined the criteria by which to decide whether there is any justification for dividing a set of observations into clusters. On the whole, we have been obliged to depend on the eye being efficient at this sort of d cision than statistical computation. In this paper, a new method is presented for dividing a set of interdependent random variables into clurters according to the degree of proximity among these random variables and essential principal components, defined by the covariance (or correlation) matrix; a non-linear functional based on the proximity is introduced, whose maximization provides the best division of these variables into cluster. A simple algorithm is proposed for construction of the clustering and also defines a random variable in each cluster...