  Two-dimensional spinless Falicov-Kimball model (FKM) with correlated hopping
is studied perturbatively in the limit of large on-site Coulomb interaction
$U$. In the neutral case the effective Hamiltonian in spin variables is derived
up to terms proportional to $U^{-3}$. Unlike the simplest FKM case, it contains
odd parity terms (resulting from the correlated hopping) in addition to even
parity ones. The ground-state phase diagram of the effective Hamiltonian is
examined in the $(a/t, h)$ plane, where $a/t$ is a parameter characterizing
strength of the correlated hopping and $h$ is a difference of chemical
potentials of two sorts of particles present in the system. It appears to be
asymmetric with respect to the change $h\to -h$ and a new ordered phase is
found for a certain interval of $a/t$.
