A neutron diffraction study has been performed on AgBr at a series of temperatures from 293 K to 706 K (melting point, T_m=701 K), including measurements as close as 0.3+or-0.05 degrees from T_m. Analysis of the structure factors using the reverse Monte Carlo modelling technique indicates that the motion of the Ag⁺ ions about their rocksalt lattice sites is anisotropic, with increasing occupancy of the (1/4 1/4 1/4) tetrahedral interstitial site as the melting point is approached. It is concluded that the silver sub-lattice is undergoing a second-order transition to a fast-ion phase in which both tetrahedral and octahedral sites are occupied (possibly similar to the fast-ion transition in the high pressure FCC phase of AgI) although melting prevents complete transition. There is a clear discontinuity in Bragg scattering at T_m, suggesting that the first-order nature of the melting transition is unaffected.