The paper focuses on the problem of classification by function decomposition within the frame of monotone classification. We propose a decomposition method for discrete functions which can be applied to monotone problems in order to generate a monotone classifier based on the extracted concept hierarchy. We formulate and prove a criterion for the existence of a positive extension of the scheme f=g(S0,h(S1)) in the context of discrete functions. We also propose a method for finding an assignment for the intermediate concept with a minimal number of values.