  We searched for an anisotropic background of gravitational waves using data
from the LIGO S4 science run and a method that is optimized for point sources.
This is appropriate if, for example, the gravitational wave background is
dominated by a small number of distinct astrophysical sources. No signal was
seen. Upper limit maps were produced assuming two different power laws for the
source strain power spectrum. For an f^-3 power law and using the 50 Hz to 1.8
kHz band the upper limits on the source strain power spectrum vary between
1.2e-48 Hz^-1 (100 Hz/f)^3 and 1.2e-47 Hz^-1 (100 Hz /f)^3, depending on the
position in the sky. Similarly, in the case of constant strain power spectrum,
the upper limits vary between 8.5e-49 Hz^-1 and 6.1e-48 Hz^-1.
  As a side product a limit on an isotropic background of gravitational waves
was also obtained. All limits are at the 90% confidence level. Finally, as an
application, we focused on the direction of Sco-X1, the closest low-mass X-ray
binary. We compare the upper limit on strain amplitude obtained by this method
to expectations based on the X-ray luminosity of Sco-X1.
