Machine for bending metal pieces (14) comprising a matrix (2) and a counter-matrix (3), wherein the matrix (2) and the counter-matrix (3) are mounted on a work surface of the machine body (10), the matrix (2) being actuatable by first drive means, and the counter-matrix (3) being in turn actuatable by second drive means. A drive member (13) enables driving the metal piece (14) and the winding thereof around a portion of the peripheral edge (8) of the matrix (2). The machine provides for a rotary encoder associated to the rotational axis (1) of the matrix (2) and a linear encoder (5, 6) associated to the translation motion of the counter-matrix (3). The matrix (2) has a complex form, different from an arc of a circle, on said portion of the peripheral edge (8). Furthermore, a CNC control system is provided, adapted to control, during the bending of the metal piece (14), both the gear motor of the matrix (2) and that of the counter-matrix (3), by means of a system with two interpolated axes based on which said linear encoder can constantly communicate with said rotary encoder. A sensor (3) is necessarily provided that is adapted to acquire, by means of self-learning and before machining the piece, the form of the peripheral edge (8) not known to the CNC system of the machine.