In this study, FeMn was introduced as an antiferromagnetic (AFM) layer to couple with a single-layered Co49Pt51 alloy thin film, and it was compared with a Co49Pt51/IrMn bilayer system in exchange bias (EB) effect, to explore the mechanism of spontaneous perpendicular exchange bias (PEB), which has been recently observed in CoPt/IrMn bilayers. Bilayers of CoPt/IrMn and CoPt/FeMn were prepared under the same conditions by sputtering at room temperature without any inducing field. Although PEB was observed in as-grown CoPt/FeMn bilayers, the loop shape and PEB behavior were found to exhibit different characteristics from those of CoPt/IrMn bilayers. The CoPt (5 nm)/FeMn (10 nm) bilayer has a sheared loop that is similar to a double-shifted loop and a much lower squareness ratio (SQR = 0.52) and exchange bias field (He = 180 Oe) than the CoPt (5 nm)/IrMn (10 nm) system, which has a rectangular loop shape and a high SQR of 0.97 and large He of 290 Oe. The two systems present entirely different dependences of PEB on the thickness of the AFM layer. CoPt/IrMn exhibits behavior that is typical of most EB systems, but for CoPt/FeMn, this dependence is more complicated with an unusual peak at an AFM layer thickness of 10 nm. Based on the dissimilar loop shapes and dependences of PEB on AFM thickness, the mechanisms of the spontaneously established PEB in these two systems are considered to differ. Investigations of cross-sectional transmission electron microscopy revealed no apparent difference between the interfacial microstructures of the two systems. X-ray diffraction studies demonstrated the ⟨111⟩ texture of both systems. Therefore, different interfacial spin configurations may be responsible for the dissimilar PEB behaviors in these two FM/AFM bilayer systems.