We conducted an experiment on radiative neutron beta decay on an intensive cold-neutron beam at ILL during April and May 2002. This work is dedicated to the analysis of the methodology and the results of the study. The main outcome of this experiment is the branching ratio (BR) for the rare neutron-decay mode in the gamma-ray quanta energy region from 35 to 100 keV. The limit obtained is BR < 6.9 x 10(-3) (90% C.L.), which is only a few permilles greater than the theoretical BR value calculated within the standard weak-interactions model. (C) 2002 MAIK "Nauka / Interperiodica".