The article deals with the problem of constructing a classifier for a set of n physical objects encoded by vectors of the space . In this well-known problem of pattern recognition, we are interested in the case when the number of factors N is much larger than the number of training vectors. As a classifier we use a linear homogeneous function . It is assumed that for each object with the number i there is a cluster set consisting of Ki training vectors corresponding to the observations of this object, for example, a set of its digitized photographs. In the case when a linear homogeneous classifier, as a rule, exists. We describe the algorithm for constructing the classifier and discuss the properties of this algorithm.