We have proposed a new Monte Carlo method for QCD at finite density. We have applied the method to the corresponding Random Matrix Theory and checked the results against the known analytical solutions. In particular our method allows us to understand how the phase of the fermion determinant induces the first order phase transition at some value of the chemical potential $\mu$. We further discuss the possibility that the $\mu \rightarrow 0$ limit may not commute with the thermodynamic limit.