  We consider the extended Hubbard model on a two-dimensional square lattice at
half-filling. The model is investigated using the strong coupling diagram
technique. We sum infinite series of ladder diagrams allowing for full-scale
charge and spin fluctuations and the actual short-range antiferromagnetic order
for nonzero temperatures. In agreement with earlier results, we find the
first-order phase transition in the charge subsystem occurring at $v=v_c\gtrsim
U/4$ with $v$ and $U$ the intersite and on-site Coulomb repulsion constants.
The transition reveals itself in an abrupt sign change of a sharp maximum in
the zero-frequency charge susceptibility at the corner of the Brillouin. States
arising at the transition have alternating deviations of electron occupations
from the mean value on neighboring sites. Due to fluctuations, these
alternating occupation deviations have short-range order. For the considered
parameters, such behavior is found for $U\lesssim5t$ with $t$ the hopping
constant. For the insulating case $U\gtrsim 6t$, in which the transition is not
observed, we find a continuous growth of the Mott gap with $v$. The evolution
of the electron density of states with increasing $v$ is also considered.
