This paper concerns the global level convergence properties of a continuous consensus protocol for multi-agent systems that evolve in continuous time on the n-sphere. The feedback is intrinsic to the n-sphere since it does not rely on the use of local coordinates obtained through a parametrization. It is shown that, for any connected undirected graph topology and all n ∈ N\{1}, the protocol yields convergence that is akin to almost global consensus in a weak sense. Simulation results suggest that almost global consensus hold. This results is of interest in the context of consensus on Riemannian manifolds since it differs from what is known with regard to 1-sphere and on SO(3) where more advanced intrinsic consensus protocols are required in order to generate equivalent results.