The spatially oscillating electron spin polarization in the Ag spacer of a 4 nm Fe/20 nmAg/4 nm Fe(001) epitaxial trilayer has been determined by means of low energy muon spin rotation. It oscillates with the same period as the interlayer exchange coupling, but shows a much weaker attenuation at large distances x from the interface. The measured magnetization profile from the inner 14 nm of the spacer is described by an oscillating polarization decaying as x(-0.8(1)). This unusual behavior may arise from a full confinement of electron states within the spacer.