We analyze primary γ-ray spectra of the odd-odd 238Np nucleus extracted from 237Npðd; pγÞ238Np coincidence data measured at the Oslo Cyclotron Laboratory. The primary γ spectra cover an excitationenergy region of 0 ≤ Ei ≤ 5.4 MeV, and allow us to perform a detailed study of the γ-ray strength as a function of excitation energy. Hence, we can test the validity of the generalized Brink-Axel hypothesis, which, in its strictest form, claims no excitation-energy dependence on the γ strength. In this work, using the available high-quality 238Np data, we show that the γ-ray strength function is to a very large extent independent of the initial and final states. Thus, for the first time, the generalized Brink-Axel hypothesis is experimentally verified for γ transitions between states in the quasicontinuum region, not only for specific collective resonances, but also for the full strength below the neutron separation energy. Based on our findings, the necessary criteria for the generalized Brink-Axel hypothesis to be fulfilled are outlined.