  We report on the search for steady point-like sources of neutral particles
around 10$^{18}$ eV between 2008 May and 2013 May with the scintillator surface
detector of the Telescope Array experiment. We found overall no significant
point-like excess above 0.5 EeV in the northern sky. Subsequently, we also
searched for coincidence with the Fermi bright Galactic sources. No significant
coincidence was found within the statistical uncertainty. Hence, we set an
upper limit on the neutron flux that corresponds to an averaged flux of 0.07
km$^{-2}$ yr$^{-1}$ for $E>1$ EeV in the northern sky at the 95% confidence
level. This is the most stringent flux upper limit in a northern sky survey
assuming point-like sources. The upper limit at the 95% confidence level on the
neutron flux from Cygnus X-3 is also set to 0.2 km$^{-2}$ yr$^{-1}$ for $E>0.5$
EeV. This is an order of magnitude lower than previous flux measurements.
