  We study the instability of charged anti-de Sitter black holes in four or
higher-dimension under fragmentation. The instability of fragmentation breaks
the black hole into two black holes. We have found that the region near
extremal or massive black holes become unstable under fragmentation. These
regions depend not only on the mass and charge of initial black hole but also
those of the fragmented one. The instability in higher-dimension is
qualitatively similar to that of four-dimension. The detailed instabilities are
numerically investigated.
