  The superradiant stability of higher dimensional non-extremal
Reissner-Nordstrom black holes under charged massive scalar perturbation is
analytically studied. We extend an analytical method developed by one of the
authors in the extremal Reissner-Nordstrom black hole cases to non-extremal
cases. Using the new analytical method, we revisit four-dimensional
Reissner-Nordstrom black hole case and obtain that four-dimensional
Reissner-Nordstrom black hole is superradiantly stable, which is consistent
with results in previous works. We then analytically prove that the
five-dimensional Reissner-Nordstrom black holes are also superradiantly stable
under charged massive scalar perturbation. Our result implies that all higher
dimensional non-extremal Reissner-Nordstrom black holes may be superradiantly
stable under charged massive scalar perturbation.
