A new version of the Method of Fundamental Solutions is proposed. Instead of locating external point sources, an external boundary should be defined, and an extension of the original solution is created by enforcing the original boundary conditions for the extended problem. This leads to a better conditioned problem than the traditional Method of Fundamental Solutions. To numerically solve the extended problem, a quadtree-based multi-level finite volume method is used, which is quite economical from the computational points of view. In addition to it, the problem of large, dense and ill-conditioned systems is completely avoided.