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In this paper, we propose a new fractal deformation technique. An “extended unit Iterated Shuffle Transformation (ext-unit-IST)” is a mapping that changes the order of the places of a code on a code space. When it is applied on a geometric space, it constructs a fractal-like repeated structure, named “local resemblance”. In our previously proposed fractal deformation technique, a geometric shape was deformed by applying an ext-unit-IST to displacement vectors (d-vectors) given on the shape. In the new technique proposed in this paper, the ext-unit-IST is applied to the increasing rates of the d-vectors. This allows the d-vectors to change widely without disturbing the shape and improves the deformation quality. Several examples demonstrate the performance of the newly proposed technique.