We study the existence of separable infinite harmonic functions in any cone of R N vanishing on its boundary under the form u(r, σ) = r −β ω(σ). We prove that such solutions exist, the spherical part ω satisfies a nonlinear eigenvalue problem on a subdomain of the sphere S N −1 and that the exponents β = β + > 0 and β = β − < 0 are uniquely determined if the domain is smooth.