In this paper we propose a method of constructing a hierarchical classification based on the notion of stochastic complexity. Minimization of stochastic complexity amounts to maximization of the information content of the classification. A dendrogram is obtained by first finding the classification which minimizes stochastic complexity and then by step-wise merging of groups such that at each step there is a minimum loss of information. The method was applied to a database containing 5313 strains of Enterobacteriaceae. The results are in reasonable accordance with present-day views on the taxonomy of Enterobacteriaceae.