Certain intervening sequence (IVS) RNAs catalyse their own excision from a primary transcript to yield mature RNA in a reaction termed self-splicing. These Group I IVS RNAs contain several conserved sequences and possess a common secondary structure. The Tetrahymena precursor ribosomal RNA possesses an IVS of this group that is known to self-splice in vitro. The nature of this IVS is of great interest to both biology and chemistry, because understanding its catalytic activity should shed new light on the function of RNA in biological systems and the evolution of RNA which might be relevant to the early stages of life on Earth. We have analysed the minimum requirement for this reaction as one approach to understanding the mechanism of this RNA catalysis. We now show that a fragment of the IVS RNA of Tetrahymena can mediate a simple transesterification reaction between the substrate GpN (where N is A, C, G or U) and the nucleophile CpU. This newly discovered reaction and its reverse reaction represent the fundamental catalytic activity of the self-splicing Group I IVSs.