After methane, ethane is the most abundant hydrocarbon in the remote atmosphere. It is a precursor to tropospheric ozone and it influences the atmosphere's oxidative capacity through its reaction with the hydroxyl radical, ethane's primary atmospheric sink. Here we present the longest continuous record of global atmospheric ethane levels. We show that global ethane emission rates decreased from 14.3 to 11.3 teragrams per year, or by 21 per cent, from 1984 to 2010. We attribute this to decreasing fugitive emissions from ethane's fossil fuel source--most probably decreased venting and flaring of natural gas in oil fields--rather than a decline in its other major sources, biofuel use and biomass burning. Ethane's major emission sources are shared with methane, and recent studies have disagreed on whether reduced fossil fuel or microbial emissions have caused methane's atmospheric growth rate to slow. Our findings suggest that reduced fugitive fossil fuel emissions account for at least 10-21 teragrams per year (30-70 per cent) of the decrease in methane's global emissions, significantly contributing to methane's slowing atmospheric growth rate since the mid-1980s.