This paper suggests novel approaches to generate exact discontinuity factors (DFs) for transverse-integrated nodal analyses with a two-by-two node configuration in a homogenized fuel assembly (FA). We have shown that the conventional DF calculation scheme cannot generate exact DFs with the nodal expansion method (NEM) calculation when a FA is subdivided into two-by-two nodes due to the inherent discrepancy between the transport-based heterogeneous analysis and the diffusion-based NEM calculation. In order to overcome the difference, an iterative, two-node NEM sweeping method is proposed. In addition, three different formulations to define a single representative DF per assembly surface for the two-by-two NEM are suggested for convenient application for the existing nodal codes while maintaining enough accuracy. Numerical assessments with a colorset model and small modular reactor cores with 16 x by x 16 FAs show that the iterative two-node NEM sweep method successfully corrects the error caused by an inherent discrepancy between the transport and the diffusion method. Among the candidates of a single representative DF, the net current weighted average DFs are found to be the most adequate.