  The partition function of the ABJM theory receives non-perturbative
corrections due to instanton effects. We study these non-perturbative
corrections, including bound states of worldsheet instantons and membrane
instantons, in the Fermi-gas approach. We require that the total
non-perturbative correction should be always finite for arbitrary Chern-Simons
level. This finiteness is realized quite non-trivially because each bound state
contribution naively diverges at some levels. The poles of each contribution
should be canceled out in total. We use this pole cancellation mechanism to
find unknown bound state corrections from known ones. We conjecture a general
expression of the bound state contribution. Summing up all the bound state
contributions, we find that the effect of bound states is simply incorporated
into the worldsheet instanton correction by a redefinition of the chemical
potential in the Fermi-gas system. Analytic expressions of the 3- and
4-membrane instanton corrections are also proposed.
