The 17-year lower-tropospheric temperature record derived from the satellite Microwave Sounding Unit (MSU) shows a global cooling trend, from 1979 to 1995, of -0.05K per decade at an altitude of about 3.5km (refs 4, 5). Air temperatures measured at the Earth's surface, in contrast, have risen by approximately +0.13K per decade over the same period,. The two temperature records are derived from measurements of different physical parameters, and thus are not directly comparable. In fact, the lower stratosphere is cooling substantially (by about -0.5K per decade), so the warming trend seen at the surface is expected to diminish with altitude and change into a cooling trend at some point in the troposphere. Even so, it has been suggested that the cooling trend seen in the satellite data is excessive,,. The difficulty in reconciling the information from these different sources has sparked a debate in the climate community about possible instrumental problems and the existence of global warming,,. Here we identify an artificial cooling trend in the satellite-derived temperature series caused by previously neglected orbital-decay effects. We find a new, corrected estimate of +0.07K per decade for the MSU-based temperature trend, which is in closer agreement with surface temperatures. We also find that the reported cooling of the lower troposphere, relative to the middle troposphere, is another artefact caused by uncorrected orbital-decay effects.