With spin-polarized scanning tunneling microscopy operating in the constant current mode, the 120^° antiferromagnetic Néel structure was found for a monolayer Mn on Ag(111) in both fcc and hcp stacking. The existence of structurally equivalent, but magnetically distinguished, Mn islands was observed. While both the fcc and hcp Mn islands display the frustrated spin structure, the orientations of their magnetic moments differ by 30^° possibly due to the spin-orbit coupling.