In this Note a new iterative method for solving the monoenergetic diffusion equation is presented. Experience has shown that the usual iterative methods used to solve the resulting equations either do not converge at all or the number of inner iterations becomes too large when a high-order approximation is used for the spatial flux. Our aim therefore has been to develop a new iterative method that leads to a small number of iterations even for a high order of spatial flux approximation. The present method is additionally expedited using Chebyshev or Wagner and Andrzejewski procedures, which are compared.The SAPHIR benchmark test case with a fixed volume source was used for calculations because it is difficult to converge. It is shown that the present method needs almost the same number of iterations for Lagrangian flux approximation of first to fourth order. This number is smaller than 53. The Chebyshev procedure, which was the most effective, halved the number of inner iterations.