We present a novel method, which we refer to as the dual minima hopping method, that allows us to find the global minimum of the potential energy surface (PES) within density functional theory for systems where a fast but less accurate calculation of the PES is possible. This method can rapidly find the ground state configuration of clusters and other complex systems with present day computer power by performing a systematic search. We apply the new method to silicon clusters. Even though these systems have already been extensively studied by other methods, we find new global minimum candidates for Si16 and Si19, as well as new low-lying isomers for Si16, Si17, and Si18.