Abstract: In quadrumodal quintic maps,it is found that there exists a global relationship between the four scaling factors αC(W),αD(W),αE(W),αF(W) and the fractal dimensions d(W) of period-|W|-tupling attractors for arbitrary quadruply superstable sequences W:d(W)log|W||αC(W)αD(W)αE(W)αF(W)|=β(4),where β(4)is a global constant independent of the concrete quadruply superstable sequence W, and |W| is the period of W.