Abstract: These transforming machines which process cardboard plates or the like for fabricating packages are comprised of two rollers defined as the die and the anvil, the die carrying the cutting and slitting knives. The plate of cardboard or the like passes between the two cylinder in such a rotary cutting die system. According to the invention, the anvil is defined by a tubular part (20) comprised of a rigid core (21) and a cut-resistant material which is cured on said core (21). The anvil (20) is divided into two complementary parts (23 and 24), one of them having a development which is slightly higher than the other one. There is incorporated a fast hooking system for connecting the two parts (23 and 24) forming the tubular part (20). The hooking system comprises an undulated tubular part (20). The hooking system comprises an undulated profile (25) in the front joining portions of both parts (23 and 24), one of them having lugs (26) which can be nested into complementary housings (27) of the other part.