Ultrahigh-energy neutrons and pions are likely to be produced in particle interactions inside cosmic ray sources and subsequently decay to neutrinos and other secondary particles [π±→μ ±νμ(ν̄μ),μ±→e ±ν̄μ(νμ)νe(ν̄e)]. In high magnetic fields of the cosmic acceleration sites, the ultrahigh-energy-charged particles may lose energy significantly due to synchrotron radiation before decay. We show that for gamma-ray bursts in the internal shock model, the flux of very high-energy antineutrinos (ν̄e) produced from decaying ultrahigh-energy neutrons can be more than the total neutrino flux produced in pion decay depending on the values of their Lorentz factors, luminosities, and variability times. © 2010 The American Physical Society.