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Time-resolved small-angle X-ray scattering (TR-SAXS) studies of the structural changes in a block copolymer after a temperature jump are reported. The sample used was a polystyrene-block-poly(ethylene-alt-butylene)-block-polystyrene (SEBS) triblock copolymer, which has a number-average molecular weight of 54000 g mol-1 and a volume fraction of polystyrene of 0.227. The film specimen was prepared by the solution-cast method using a selective solvent. The as-cast specimen with lamellar microdomains underwent the temperature jump from 363 to 403 K and the morphological transition from lamellae to cylinders was observed as a function of time by the TR-SAXS technique. The singular value decomposition (SVD) analysis was performed on the scattering profiles. This analysis strongly suggested the existence of a third basis component of the X-ray scattering profiles, thus supporting that there is an intermediate state during the transition from lamellae to cylinders.