The dependence of the inelastic lifetime of electrons in the image-potential states of Cu(100) on their momentum parallel to the surface has been studied experimentally by means of time- and angle-resolved two-photon photoemission and theoretically by evaluating the electron self-energy within the GW approximation. The pronounced decrease of the n = 1 lifetime from 40 fs at normal emission (k(parallel) = 0) to 20 fs for k(parallel) = 0.33 A(-1) cannot be accounted for by interband decay processes to bulk states. We show that intraband transitions within the image-state band give a contribution to this decrease comparable in magnitude with the interband channel.