The evolution of the Earth's atmosphere is marked by a transition from an early atmosphere with very low oxygen content to one with an oxygen content within a few per cent of the present atmospheric level. Placing time constraints on this transition is of interest because it identifies the time when oxidative weathering became efficient, when ocean chemistry was transformed by delivery of oxygen and sulphate, and when a large part of Earth's ecology changed from anaerobic to aerobic. The observation of non-mass-dependent sulphur isotope ratios in sedimentary rocks more than approximately 2.45 billion years (2.45 Gyr) old and the disappearance of this signal in younger sediments is taken as one of the strongest lines of evidence for the transition from an anoxic to an oxic atmosphere around 2.45 Gyr ago. Detailed examination of the sulphur isotope record before 2.45 Gyr ago also reveals early and late periods of large amplitude non-mass-dependent signals bracketing an intervening period when the signal was attenuated. Until recently, this record has been too sparse to allow interpretation, but collection of new data has prompted some workers to argue that the Mesoarchaean interval (3.2-2.8 Gyr ago) lacks a non-mass-dependent signal, and records the effects of earlier and possibly permanent oxygenation of the Earth's atmosphere. Here we focus on the Mesoarchaean interval, and demonstrate preservation of a non-mass-dependent signal that differs from that of preceding and following periods in the Archaean. Our findings point to the persistence of an anoxic early atmosphere, and identify variability within the isotope record that suggests changes in pre-2.45-Gyr-ago atmospheric pathways for non-mass-dependent chemistry and in the ultraviolet transparency of an evolving early atmosphere.