A new mechanism is proposed to explain the origin of negative differential resistance (NDR) in a strongly coupled single molecule-metal junction. A first-principles quantum transport calculation in a Fe-terpyridine linker molecule sandwiched between a pair of gold electrodes is presented. Upon increasing the applied bias, it is found that a new phase in the broken symmetry wave function of the molecule emerges from the mixing of occupied and unoccupied molecular orbitals. As a consequence, a nonlinear change in the coupling between the molecule and the lead is evolved resulting in NDR. This model can be used to explain NDR in other classes of metal-molecule junction devices.