Method to transform a rolling mill in order to revamp an old-type rolling line (10) fed by slabs with a thickness greater than 160 mm and arriving from an accumulation store (12) and to insert a segment of new line comprising at least a continuous casting machine (19) to produce thin and medium slabs, with attached relative operating assemblies such as extraction, straightening, shearing devices etc., the old line (10) comprising a roughing unit with one or more stands and a terminal segment (21) with a finishing train (15), a cooling area (17), systems to collect the product (18a, 18b) etc., the segment of new line (110) being achieved and installed in a position near the old line (10) while the old line (10) continues working, the segment of new line (110) being equipped substantially at the terminal end with a movable element (120) in order to be at least temporarily connected to the terminal end (21) of the old line (10).