  We apply the recently proposed quantum extremal surface construction to
calculate the Page curve of the eternal Reissner-Nordstr\"om black holes in
four dimensions ignoring the backreaction and the greybody factor. Without the
island, the entropy of Hawking radiation grows linearly with time, which
results in the information paradox for the eternal black holes. By extremizing
the generalized entropy that allows the contributions from the island, we find
that the island extends to the outside the horizon of the Reissner-Nordstr\"om
black hole. When taking the effect of the islands into account, it is shown
that the entanglement entropy of Hawking radiation at late times for a given
region far from the black hole horizon reproduces the Bekenstein-Hawking
entropy of the Reissner-Nordstr\"om black hole with an additional term
representing the effect of the matter fields. The result is consistent with the
finiteness of the entanglement entropy for the radiation from an eternal black
hole. This facilitates to address the black hole information paradox issue in
the current case under the above-mentioned approximations.
