Let M be a smooth, compact, oriented, odd-dimensional Riemannian manifold and let Γ → Mˆ → M be a normal covering of M. It is proved that the relative von Neumann eta-invariant ρ(2)(Mˆ) of Cheeger and Gromov is a homotopy invariant when Γ is torsion-free, discrete and the Baum–Connes assembly map μmax[ratio ]K0(BΓ) → K0(C*Γ) is an isomorphism.