This study extends the research on the convergence analysis of energy-related variables to cover renewable energy intensity by focusing on 26 OECD countries from 1990 to 2021. While there have been several studies on the convergence of different energy variables including renewable energy, the intensity dimension has been largely ignored in the literature. As some non-zero carbon emissions are associated with deploying various forms of renewable energy resources, ignoring their intensity of GDP fails to address the question of efficiency. To address this gap, this study employed a battery of econometric techniques including the novel panel unit root tests that capture abrupt or smooth breaks in the presence of cross-sectional dependence to test for the presence of unit roots in relative renewable energy intensity. The study also examined different clusters of the sample to check the existence of convergence or otherwise at different levels. The results suggest that 21 countries are convergent and only Germany, Japan, Netherlands, Poland and Switzerland are not convergent when the full sample is considered. However, these countries are convergent when other clusters of the countries are examined. Policy implications of the study have been discussed in the paper