A new approach for constructing nonoverlapping domain decomposition based preconditioners for conjugate gradient methods is presented. The main idea, which is realized, is the approximation of the spectrum of the Schur complement by simple functions, such as rational functions, which leads to solving a lower dimensional interface problem. The basic ideas are illustrated on the simplest two-subdomains domain decomposition for the Poisson equation with Dirichlet boundary conditions on a rectangle. The problem is discretized by the 5-point star finite difference scheme or a linear finite element Galerkin approximation on an uniform grid. The new family of preconditioners is constructed by variants of function approximation of the function, which is characterized by the spectrum of the Schur complement according to the nodes on the boundary of the spatial domain. The eigen-decomposition theory for the Schur complement is extended to the nonuniform grid case. By applying the rational approximations to this theory a simple, efficient in computation and effective in convergence approach, is obtained.