The presence of mass-independently fractionated sulphur isotopes (MIF-S) in many sedimentary rocks older than approximately 2.4 billion years (Gyr), and the absence of MIF-S in younger rocks, has been considered the best evidence for a dramatic change from an anoxic to oxic atmosphere around 2.4 Gyr ago. This is because the only mechanism known to produce MIF-S has been ultraviolet photolysis of volcanic sulphur dioxide gas in an oxygen-poor atmosphere. Here we report the absence of MIF-S throughout approximately 100-m sections of 2.76-Gyr-old lake sediments and 2.92-Gyr-old marine shales in the Pilbara Craton, Western Australia. We propose three possible interpretations of the MIF-S geologic record: (1) the level of atmospheric oxygen fluctuated greatly during the Archaean era; (2) the atmosphere has remained oxic since approximately 3.8 Gyr ago, and MIF-S in sedimentary rocks represents times and regions of violent volcanic eruptions that ejected large volumes of sulphur dioxide into the stratosphere; or (3) MIF-S in rocks was mostly created by non-photochemical reactions during sediment diagenesis, and thus is not linked to atmospheric chemistry.