In March 1991 35 control points were measured in the collision zone between the Indian and Asian plates using the Global Positioning System (GPS). Twenty‐eight points are located in the Nepal Himalaya, and 7 in S. and E. Tibet. In October 1992, 6 of the Nepal points were remeasured together with 3 bedrock points in Bihar State, India, 5 points in E. Tibet, and one in Urumchi. The average WRMS GPS position repeatability between 1991 and 1992 improved from 8 mm to 5 mm in the north, 16 mm to 7 mm in the east, and 32 mm to 25 mm in the vertical components. Himalayan convergence rates of 20 mm/yr may be resolved to 10% accuracy within 5 years with these uncertainties. Unless improved vertical measurement techniques are introduced many decades must elapse before regional secular vertical motions may be resolved. The 1991.3–1992.8 measurements are consistent with geologically determined Himalayan convergence rates of less than 20 mm/year.