A tire-changing machine comprising support means (4) for a wheel, a tool-bearing arm (50) at an end of which a bead-breaking tool (6) is hinged according to a hinge axis (E) which is perpendicular to an axis (A) of the wheel, and first motorised means (32, 33) for causing a relative movement, in a parallel direction to the axis (A) of the wheel, between the support means (4) and the tool-bearing arm (50), such as to press the bead-breaking tool (6) against a flank of a tire on the wheel, characterized in that it comprises second motorised means (64), activatable independently from the first motorised means (32, 33), which second motorised means (64) are destined to rotate the bead-breaking tool (6) about the hinge axis (E) with the tool-bearing arm (50), in order to vary an inclination of the bead-breaking tool (6) with respect to the axis (A) of the wheel which is mounted on the support means (4).