  We investigated the Goon--Penco (GP) relation on higher-dimensional
Reissner-Nordstr\"om black holes with an arbitrary cosmological constant. It
was found that the GP relation retained its form in four- and
higher-dimensional spacetimes. Thus, the reactions in the black holes are
universal with respect to the dimensionality. Furthermore, the GP relation was
found to be universal on any state of the black hole including near-extremal
and near-Nariai cases. Thus, this study showed that the GP relation was
prevalent for higher-dimensional Reissner-Nordstr\"om black holes with an
arbitrary cosmological constant regardless of the initial state.
