A method and machine for removing a tire, fitted with a rigid inner run-flat ring, from a relative rim, whereby, once the rim and the tire are fixed onto a turntable having a central hub and rotating about a first axis coaxial with the hub and the tire, a bead of the rigid inner ring is engaged and moved axially outwards of a relative flange of the rim by a hook carried by a lever hinged to the hub and oscillated, with respect to the hub and in a radial plane of the turntable, about a second axis perpendicular to the first axis and rotating about the first axis.