  Quantum theory of 2d gravity for $c>1$ is examined as a non-critical string
theory by taking account of the loop-correction of open strings whose end
points are on the 2d world surface of the closed string. This loop-correction
leads to a conformal anomaly, and we obtain a modified target-space action
which implies a new phase of the non-critical closed-string. In this phase, the
dual field of the gauge field, which lives on the boundary, condenses and the
theory can be extended to $c>1$ without any instability.
