A new methodology that is applicable to individual nuclides is developed for the determination of the intermediate resonance (IR) parameters in the multigroup formalism. The method keeps the main steps commonly used for the determination of these parameters and is compatible with the methods utilized for the generation of the multigroup libraries for thermal and epithermal reactors. The proposed method does not impose any restriction on the formalism used to describe the resonances. Use is made of the computational approach used by the GROUPR module of the NJOY system (flux calculator option). A numerical scheme is presented to determine the IR parameters by means of an iterative approach. Numerical results for the IR parameters in a heterogeneous system composed of UO2 (238U only) and hydrogen as an external moderator are reported as a function of the dilution 0, heterogeneity factor , and temperature T for several epithermal groups of the MUFT structure. The results are consistent, as shown by the consistency checks performed.