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In this paper we study the four-point correlation function of the energy–momentum supermultiplet in theories with N = 4 superconformal symmetry in four dimensions. We present a compact form of all component correlators as an invariant of a particular abelian subalgebra of the N = 4 superconformal algebra. This invariant is unique up to a single function of the conformal cross-ratios which is fixed by comparison with the correlation function of the lowest half-BPS scalar operators. Our analysis is independent of the dynamics of a specific theory, in particular it is valid in N = 4 super Yang–Mills theory for any value of the coupling constant. We discuss in great detail a subclass of component correlators, which is a crucial ingredient for the recent study of charge-flow correlations in conformal field theories. We compute the latter explicitly and elucidate the origin of the interesting relations among different types of flow correlations previously observed in arXiv:1309.1424.