It is shown, for a model numerical experiment, that the diamond difference (DD) solution of the x,y geometry discrete ordinates equations, with a fixed angular quadrature set, converges in the norm with less than a second-order convergence rate as the spatial mesh is refined, and that the value of this convergence rate depends on the definition of the error norm. However, this same experiment suggests that numerical integrals of DD solution do converge with a secondorder convergence rate.