PROGS2H4 - the program for solving the boundary problem for the system of differential equations. The description of the computational scheme and procedure realizing the sweep method for solving the system of two ordinary differential equations with 2nd type boundary conditions at the ends points of given interval is represented. The boundary problem is approximated with the help of the difference scheme of O(h4) precision on the mesh with constant step h. This problem occurs in schemes of linearity of nonlinear boundary problems (for example, in Newtonian iterative schemes), and represented. (author)