Counter-matrix having a removable insert at an end and a roller at the other end, wherein the roller, exerting, an annular groove thereof, only the function of guiding the metal pipe being processed and by eliminating any sliding friction with the pipe, reduces the strain of the pipe bending machines. The insert has a semi-cylindrical work surface with a smaller radius or equivalent to the nominal external radius of the pipe. The insert is preferably tilted with respect to the geometric axis of the pipe or metal section, coinciding with the insertion direction of the pipe in the pipe bending machines