The magnitude 7.8 Gorkha earthquake in April 2015 ruptured a 150-km-long section of the Himalayan décollement terminating close to Kathmandu. The earthquake failed to rupture the surface Himalayan frontal thrusts and raised concern that a future Mw ≤ 7.3 earthquake could break the unruptured region to the south and west of Kathmandu. Here we use GPS records of surface motions to show that no aseismic slip occurred on the ruptured fault plane in the six months immediately following the earthquake. We find that although 70 mm of afterslip occurred locally north of the rupture, fewer than 25 mm of afterslip occurred in a narrow zone to the south. Rapid initial afterslip north of the rupture was largely complete in six months, releasing aseismic-moment equivalent to a Mw 7.1 earthquake. Historical earthquakes in 1803, 1833, 1905 and 1947 also failed to rupture the Himalayan frontal faults, and were not followed by large earthquakes to their south. This implies that significant relict heterogeneous strain prevails throughout the Main Himalayan Thrust. The considerable slip during great Himalayan earthquakes may be due in part to great earthquakes tapping reservoirs of residual strain inherited from former partial ruptures of the Main Himalayan Thrust.