We prove a theorem that characterizes a two-parameter family of solutions to Einstein equations with a negative cosmological constant, representing, in general, non-spherical radiating black holes in an anti-de Sitter background. It is shown that the best known non-spherical radiating black hole solutions are particular cases and static non-spherical black hole solutions, for Type I fluid, are also retrieved. A brief discussion on the energy conditions, singularities and horizons is provided.