  We derive the nonperturbative effect in type 0B string theory, which is
defined by taking the double scaling limit of a one-matrix model with a two-cut
eigenvalue distribution. However, the string equation thus derived cannot
determine the nonperturbative effect completely, at least without specifying
unknown boundary conditions. The nonperturbative contribution to the free
energy comes from instantons in such models. We determine by direct computation
in the matrix model an overall factor of the instanton contribution, which
cannot be determined by the string equation itself. We prove that it is
universal in the sense that it is independent of the detailed structure of
potentials in the matrix model. It turns out to be a purely imaginary number
and therefore can be interpreted as a quantity related to instability of the
D-brane in type 0 string theory. We also comment on a relation between our
result and boundary conditions for the string equation.
