A sheet metal bending machine includes a sheet metal presser defining a first support surface supporting a first sheet metal portion, a bending punch movable with respect to the first support surface between a passive position, in which it is raised with respect to the first support surface, and an active position, in which it is pressed against the first support surface to lock the first sheet metal portion on the sheet metal presser with a punch edge, and a bending die defining a second support surface. The presser and the die are movable with respect to one another substantially in parallel with a direction transverse to the first and second bending edges to switch from the partial to a complete sheet metal bending configuration, in which the distance is reduced to press partially curved section towards said punch edge, thereby deforming it further and increasing the curvature of sheet.