  The fragmentation of black hole containing $f(R)$ global monopole under GUP
is studied. We focus on that the black hole breaks into two parts. We derive
the entropies of the initial black hole and the broken parts while the
generalization of Heisenberg's uncertainty principle is introduced. We find
that the $f(R)$ global monopole black hole keeps stable instead of breaking
because the entropy difference is negative without the generalization. The
fragmentation of the black hole will happen if the black hole entropies are
limited by the GUP and the considerable deviation from the general relativity
leads the case that the mass of one fragmented black hole is extremely small
and the other one is extremely large.
