  We have studied the quantum Liouville theory on the Riemann sphere with n>3
punctures. While considering the theory on the Riemann surfaces with n=4
punctures, the quantum theory near an arbitrary but fixed puncture can be
obtained via canonical quantization and an extra symmetry is explored. While
considering more than four distinguished punctures, we have found the exchange
relations of the monodromy parameters from which we can get a reasonable
quantum theory.
