A novel global flux surface hopping (GFSH) approach is proposed. In this method, the surface hopping probabilities rely on the gross population flow between states, rather than the state-to-state flux as in the standard fewest switches surface hopping (FSSH). GFSH captures the superexchange mechanism of population transfer, while FSSH lacks this capability. In other aspects, including minimization of the number of hops, internal consistency, velocity rescaling, and detailed balance, the GFSH algorithm is similar to FSSH. The advantages of GFSH are demonstrated with a model 3-level system and an Auger process in a semiconductor quantum dot. Current studies indicate that GFSH can replace FSSH, but further tests are needed.