  Combining the recent scanning tunneling microscopy (STM) and angle-resolved
photoemission spectroscopy (ARPES) measurements, we construct a tight-binding
model suitable for describing the band structure of monolayer FeSe grown on
SrTiO$_{3}$. Then we propose a possible pairing function, which can well
describe the gap anisotropy observed by ARPES and has a hidden sign-changing
characteristic. At last, as a test of this pairing function we further study
the nonmagnetic impurity-induced bound states, to be verified by future STM
experiments.
