A unique three-stage transformation behaviour on cooling has been observed in a Ti-50.2 at % Ni alloy after a low temperature ageing treatment. The cooling transformation in the aged alloy occurred as a three-stage process of austenite-to-R phase transition followed by two separate martensitic transformations. The R phase transition developed during ageing with a clear second order nature initially and gradually evolved into a predominantly first order process. The occurrence of the R transition is not associated with a decrease in the martensitic transformation temperature during ageing. The reverse transformation to austenite occurred in one step, regardless of the nature of the forward transformation on cooling. An all-round shape memory effect was observed in aged samples. These experimental observations suggest that precipitation induced by the ageing treatment is responsible for the unusual transformation behaviour.