We report a giant perpendicular exchange bias Hexper exhibited in the R-H curves of an inverted (Co/Pt)n/Co/IrMn multilayer and an inverted (Co/Pt)n/Co/Cu/(Co/Pt)4/Co/IrMn spin-valve structure, in which the Pt layers are only 1/4 nm in thickness and thinner than the Co layers. Hexper shows an unusual linear scaling with the repetition n+1 of the (Co/Pt)n/Co free layer, reaching 792 Oe for n+1=9. In contrast, the in-plane exchange bias Hexin is almost constant. This effect originates from Co/IrMn interfacial magnetic coupling in the inverted (Co/Pt)4/Co/IrMn reference layer and is magnified by a near-perpendicular exchange coupling between the interface Co layer and the multilayer (Co/Pt)n (n=4 for the spin-valve structures) in the reference layer. The latter also leads to a linear scaling of the exchange bias with the number of repetitions of Co/Pt in the reference layer.