We use Global Positioning System (GPS) measurements acquired from 1991 to 1995 to constrain the motion of sites in Bangalore, in southern India, and Kathmandu, Nepal, relative to a global GPS network. These measurements permit estimates of the northward motion of the Indian plate and convergence between the southern Himalaya and the Indian subcontinent. The velocities of Bangalore and Kathmandu in the ITRF92 reference frame agrees with that predicted by the NNR‐NUVEL1A plate motion model for Indian plate motion, and differ from that predicted for the Australian plate, confirming the independent motion of the Indian and Australian plate fragments. No significant motion was detected between Bangalore and Kathmandu during the three years from 1991–1994, even though Kathmandu is located in the hanging wall of the active Himalayan thrust system. The Himalayan thrust system is thought to accommodate 18±7 mm/yr of convergence and has been the source of several historic M ∼ 8 earthquakes. The absence of motion of Kathmandu relative to the Indian plate can be explained if the thrust system is presently locked south of the Greater Himalaya. Our preferred model has no steady slip on the detachment south of the Greater Himalaya, and steady slip at a rate greater than 6 mm/yr (1/3 of the long‐term convergence rate) can be ruled out at 95% confidence level.