  Inelastic neutron scattering measurements have been performed on a
superconducting single crystal FeTe$_{0.5}$Se$_{0.5}$ to examine the ${\bf
Q}$-dependent enhancement of the dynamical structure factor, $S({\bf Q},E)$,
from ${\bf Q}$ = (0, 0) to ($\pi$, $\pi$), including ($\pi$, 0) in the
superconducting state. In most of iron-based superconductors, $S({\bf Q},E)$ is
enhanced at ${\bf Q}$ = ($\pi$, 0), where the "magnetic resonance mode" is
commonly observed in the unfolded Brillouin zone. Constant-$E$ cuts of $S({\bf
Q},E)$ suggest that the enhancement is not uniform in the magnetic excitation,
and limited around ${\bf Q}$ = ($\pi$, 0). This result is consistent with the
theoretical simulation of the magnetic resonance mode due to the
Bardeen$-$Cooper$-$Schrieffer coherence factor with the sign-reversing order
parameter of s$_{\pm}$ wave.
