The Chebyshev Gauss-Radau discrete version of the polar-diffusion operator, presents complex conjugate eigenvalues when it is associated with Neumann boundary condition imposed at r = 1. It is shown that this ellipticity violation of the original continuous problem is genuine and not due to some round-off error. A way to avoid these complex conjugate eigenvalues is proposed, at the expense of some loss of accuracy. An evaluation is performed of the impact this approach has on the spectral accuracy of the solution.