  An analytical work on intrinsic localized modes in a two-dimensional
Heisenberg ferromagnet on the checkerboard lattice is presented. Taking
advantage of an asymptotic method, the governing lattice dynamical equations
are reduced to one (2+1) -dimensional nonlinear Schr\"odinger. In our work, we
obtain two types of nonlinear localized mode solutions, namely, Brillouin zone
center modes and Brillouin zone corner modes. The occurrence conditions for
these intrinsic localized modes are given in detail. Especially, we find that
the competition between the Dzialozinskii-Moriy interaction and the
next-nearest neighbor interaction of the checkerboard ferromagnet has an effect
on the local structure of the Brillouin zone corner acoustic mode.
