Rapid boron dilution transients have shown the need for accurate knowledge of the solute particle distribution in pressurized water reactors (PWRs). Small-break loss-of-coolant accidents (SBLOCAs) enable the formation of low-borated slugs in the loop seals. Low-borated water, if driven to the core, could cause a reactivity excursion. Since online boron concentration measurement is impractical in the primary system of PWR plants and quite difficult in test facilities, best-estimate codes should be seen as the most suitable tools. However, transport of a low-borated slug through the primary system requires accuracy of the methods. Several studies have shown high numerical diffusion introduced by the upwind difference schemes habitually used by system codes. Furthermore, most of the boron tracking models implemented in system codes at present do not consider physical diffusion. Nevertheless, to introduce physical diffusion, it is necessary to considerably reduce numerical diffusion. The implicit Godunov scheme, which is available in RELAP5, has proved its capability in almost eradicating numerical diffusion. However, the formulated equation in RELAP5 does not deal with physical diffusion. A new tracking model for the solute field is presented, along with results of its implementation in the RELAP5 code. To evaluate the new model, a numerical test has been performed that demonstrates both the reduction of numerical diffusion and the correct simulation of physical diffusion. Moreover, the UPC model has shown its consistency in experiment F1.1, which is an SBLOCA with boron dilution. The test was part of the OECD-PKL2 program directed by the Organisation for Economic Cooperation and Development (OECD).