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A pipe bending machine comprising a bending assembly (1), a support arm (2), and a spindle positionable toward an annular pipe; which is characterized in that the arm is pivotedly supported swingingly relative to the bending assembly through a pivot (6), slidably supported along a stem (7) on the axis passing through the center of rotation of the matrix and the center of swinging of the countermatrix assembly, so as to automatically position itself on the zero.