A two-dimensional hierarchical lattice is considered, in which an elementary cell is represented by the vertices of a square. In the generalized hierarchical model, the distance between opposite vertices of a square differs from the distance between neighboring vertices and is a parameter of the new model. At each vertex of the lattice, the field is defined by a set of 4 generators of the Grassmann algebra. The Hamiltonian of the field is described by the interaction of the 4-th degree. The transformation of the renormalization group in the space of coupling coefficients defining this interaction is defined as a nonlinear mapping. All branches of fixed points of this mapping are described.