In this paper, we suggest a new way to identify single bright sources of
Ultra High Energy Cosmic Rays (UHECR) on the sky, on top of background. We look
for doublets of events at the highest energies, E > 6 x 10^19 eV, and identify
low energy tails, which are deflected by the Galactic Magnetic Field (GMF). For
the sources which are detected, we can recover their angular positions on the
sky within one degree from the real ones in 68% of cases. The reconstruction of
the deflection power of the regular GMF is strongly affected by the value of
the turbulent GMF. For typical values of 4 microG near the Earth, one can
reconstruct the deflection power with 25% precision in 68% of cases.Comment: 20 pages, 10 figures. Corresponds to the version published in JCA