We report the observation of a reversible thermotropic transition between the lamellar and cylindrical morphologies in a polystyrene-poly(ethene-co-butene) diblock copolymer. The nature of the intermediate structures which form as the transition progresses has been examined using two-dimensional small-angle X-ray scattering (SAXS) and transmission electron microscopy (TEM). Results show that the transformation from the lamellar to the cylindrical morphology proceeds in two steps. Initially, fluctuations along the interface joining the components of the copolymer grow in amplitude until the lamella transforms into a sheet of evenly spaced cylinders; cylinders which form in adjacent lamellae are usually in poor register with one another. This intermediate structure subsequently anneals into the hexagonal packing of cylinders characteristic of the cylindrical morphology. The reverse transition from cylinders to lamellae proceeds without producing any intermediate signature detectable by SAXS.