Core collapse of massive stars and binary neutron stars or black hole neutron star binary mergers are likely progenitors of long and short duration gamma-ray bursts respectively. Neutronized material in the former and neutron star material in the latter are ejected by the central engine implying a neutron-rich jet outflow. A free neutron, however, beta decays to a proton, an electron (beta) and an anti-neutrino in about fifteen minutes in its rest frame. Sudden creation of a relativistic electron is accompanied by radiation with a unique temporal and spectral signature. We calculate here this radiation signature collectively emitted by all beta decay electrons from neutron-rich outflow. Detection of this signature may thus provide strong evidence for not only neutron but also for proton content in the relativistic gamma-ray burst jets.