Field condensation and a possible phase in a non-critical string for c>1

A possible existence of the quantum theory of two-dimensional gravity for c > 1 is examined as a non-critical string theory by taking account of the loop correction of open strings whose endpoints are on the two-dimensional world surface of the closed string. This loop correction leads to a conformal anomaly, from which we obtain a modified target-space action which implies a new phase of the non-critical closed string. For c = 2, we could explicitly show the possibility of a massless tachyon phase.