A method of discrete representation of thermal-neutron spectra, especially suitable for U-Pu systems has been developed. The energy points and corresponding integration weights have been determined so as to provide accurate reaction rates in U-Pu lattices, the total number of points being considerably less than the necessary number of groups in multigroup treatment. Furthermore, a convenient method of scattering matrix construction has been proposed and the system of multipoint equations, formally identical to multigroup equations, has been derived. The proposed method has been tested by calculating thermal reaction rates and energy spectra in a pin cell and comparing with the group method. Some results are given in the present paper. The authors' experience is that in all practical cases 15 points are as good as 40 energy groups for calculating fuel reaction rates in the energy region below 2 eV.