  We present a new method for calculating arrival distribution of UHECRs
including modifications by the galactic magnetic field. We perform numerical
simulations of UHE anti-protons, which are injected isotropically at the earth,
in the Galaxy and record the directions of velocities at the earth and outside
the Galaxy for all of the trajectories. We then select some of them so that the
resultant mapping of the velocity directions outside the Galaxy of the selected
trajectories corresponds to a given source location scenario, applying
Liouville's theorem. We also consider energy loss processes of UHE protons in
the intergalactic space. Applying this method to our source location scenario
which is adopted in our recent study and can explain the AGASA observation
above 4 \times 10^{19} eV, we calculate the arrival distribution of UHECRs
including lower energy (E>10^19 eV) ones. We find that our source model can
reproduce the large-scale isotropy and the small-scale anisotropy on UHECR
arrival distribution above 10^19 eV observed by the AGASA. We also demonstrate
the UHECR arrival distribution above 10^19 eV with the event number expected by
future experiments in the next few years. The interesting feature of the
resultant arrival distribution is the arrangement of the clustered events in
the order of their energies, reflecting the directions of the galactic magnetic
field. This is also pointed out by Alvarez-Muniz et al.(2002). This feature
will allow us to obtain some kind of information about the composition of
UHECRs and the magnetic field with increasing amount of data.
