For calculating the fine flux distribution in heterogeneous fuel rod lattices, an exact treatment of the geometry and the use of a high-order approximation of the transport theory is needed. For this purpose, a discrete ordinates solution of the neutron transport equation for mixed geometry has been developed. The discretization of the space is performed in separate one-dimensional cylindrical coordinate systems, imbedded in a two-dimensional rectangular mesh grid. The geometrical link between the cylindrical and the rectangular systems is achieved by approximating the outer circle of each cylindrical system by a polygon with side numbers ≥8. Thus, each cylindrical geometry is enclosed in a two-dimensional mesh grid consisting of rectangles, trapeziums, and triangles. Because of the different orientation of the angular segmentation in XY and R coordinates, transfer coefficients are derived to calculate the directional flux distribution on the boundary between both systems. A special set of equal-weighted quadrature coefficients (EQn) is used to get transfer coefficients, providing a fast and accurate solution. The method is realized in a program called DOXCY, which runs within the nuclear program system RSYST. The program is verified on selected benchmark problems. The numerical results are given, showing the advantages and limits of the method.