— The spectra of the majority of bursts exhibit a low-energy power law index, α, that is either a constant or becomes softer with time. However, in the burst of 30 May 1996 α becomes harder. Here we show that this behavior can be explained by a hybrid model consisting of a thermal and a non-thermal component. In this burst the power-law index of the non-thermal component changes drastically from s ∼ −1.5 to s ∼ −0.67 at approximately 5 seconds after the trigger, thereby revealing, at low energies, the thermal component with its hard Rayleigh-Jeans tail. This leads to the large α-values that are found if the Band function is fitted to the spectra. We suggest that the change in s could be due to a transition from fast to slow cooling of the electrons emitting in the BATSE range. This could be due to the fact that the magnetic field strength becomes weaker.