Mop wringer machine that incorporates the classic wringer basket (2), mounted as a floating basket on its frame or base (1), by means of springs, therefore when a pair of flaps (4) in the shape of U puts pressure on the mop, after this is entered into the wringer basket (2), this basket is capable of being moved downward in a springing motion, in order to absorb different pressures caused by mops (5) of different shapes and/or sizes.