  We show that the deep expected in the diffuse photon spectrum above the
threshold of e+e- pair production, i.e., at energies 10^15 - 10^17 eV, may be
absent due to the synchrotron radiation by the electron component of the
extragalactic Ultra-High Energy Cosmic Rays (UHE CR) in the Galactic magnetic
filed. The mechanism we propose requires small (less than 2x10^-12 G)
extragalactic magnetic fields and large fraction of photons in the UHE CR. For
a typical photon flux expected in top-down scenarios of UHE CR, the predicted
flux in the region of the deep is close to the existing experimental limit. The
sensitivity of our mechanism to the extragalactic magnetic field may be used to
improve existing bounds on the latter by two orders of magnitude.
