A machine for forming metal stampings comprising an upper die holder on which an upper die half and an upper clamping yoke are mounted; a lower die holder on which a lower die half and a lower clamping yoke are mounted; handling means suitable to achieve the bringing together and moving apart of the upper die holder and the lower die holder; and an edge cutting/bending unit suitable to carry out both the cutting and bending of the edge and arranged between the two die halves and the two clamping yokes. The edge cutting/bending unit comprises a cutting blade suitable to cut the edge of a sheet to be formed; an outer bending blade arranged below said cutting blade and which forms a pushing step with it, facing in use towards said upper die half and said lower die half, and an inner bending blade arranged to slide along said outer bending blade.