This paper extends my previous analysis of the causal relationship of GDP and energy use in the USA in the post-war period to a cointegration analysis of that relationship. It is found that the majority of the relevant variables are integrated justifying a cointegration analysis. The results show that cointegration does occur and that energy input cannot be excluded from the cointegration space. The results are plausible in terms of macroeconomic dynamics. The results are similar to my previous Granger Causality results and contradict claims in the literature (based on bivariate models) that there is no cointegration between energy and output.