Many classification problems can be successfully solved by the decision tree method. In the classical formulation, at each node of a tree, a decision is made based on a value of only one feature, and therefore the trees are cumbersome and difficult to perceive. The article proposes a new machine learning approach - a tree of secant hyperplanes. The basic idea of a decision tree is that the hierarchical logical rules are preserved, but the decision at each node is made based on the secant hyperplane, which significantly reduces the size of the tree. To solve this problem, programs of partial-integer mathematical programming can be used. The key difference between the proposed approach and other methods is the use of the Relu 1 function in each node. This method is based on the theory of committee machine decisions of the Ural School of Pattern Recognition of the Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences. The article describes the algorithm to construct a tree of secant hyperplanes and presents the results of classification on data from the UCI repository.