Grinding machine for machining sheets of glass; in the machine, a sheet which has one of its own perimeter edges which is at least partially to be ground, is advanced on a horizontal plane, through a single work station, where the sheet itself is disposed in an unambiguous reference position on the plane, relative to a support structure, it is held in the reference position itself by a plurality of suckers, and is ground by motorized grinding heads; the machine is provided with actuators for vertically displacing the suckers and, therefore, the sheet of glass between a lowered rest position and a raised position in which the sheet is ground.