We report the detection of proper motions in [Fe ii] 1.644 µm emission among the southeasternmost features in the Herbig-Haro object complex GGD 37. Imaging observations were made over a period of 5 yr, at epochs 1993.67, 1996.71, and 1998.68, that reveal proper-motion velocities of 400+/-200 km s-1 at GGD 37:W2 and 850+/-200 km s-1 at a newly identified object, designated GGD 37:RWPF 1. We believe the proper-motion velocity of GGD 37:RWPF 1 is the highest found to date for a Herbig-Haro object. The direction of GGD 37:RWPF 1's proper motion is almost due west, away from the nearby young stellar object complex in Cep A East. GGD 37:W2's direction of proper motion is north/northwest, which does not lead back to any of the compact objects in Cep A East.