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.
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