A new nodal method HEXNEM2 for hexagonal geometry is described. The method is based on a two-dimensional expansion of the intranodal fluxes. Polynomials up to the second order and exponential functions are used in each group. By this method, the singular terms occurring in the transverse integration methods are avoided. Side-averaged and corner-point values of fluxes and currents are used for the coupling of nodes. A calculation scheme for the outgoing partial currents at the sides and similar expressions for the corners from given incoming values are used in the inner iteration, which gives a fast-running scheme. The method is tested against two-dimensional hexagonal benchmark problems for the VVER-type reactors. The results show that the multiplication factor and nodal powers are predicted accurately. A considerable improvement can be shown in the results for the VVER-1000 benchmarks compared with the method developed previously for the code DYN3D and the simpler method HEXNEM1.