  We investigate the effect of the $RF^2$ correction on the holographic
superconductor model in the background of AdS black hole. We find that, similar
to the effect caused by the Weyl correction, the higher $RF^2$ correction term
can make it easier for the scalar operator to condense and result in the larger
deviations from the expected relation in the gap frequency. However, if a
non-trivial hair for the black hole has been triggered, we observe that the
$RF^2$ correction and the Weyl correction do play different roles in the
behavior of the condensation, which can be used to support the existing
findings.
