When best-estimate calculations are performed, the uncertainties need to be quantified. Worldwide, various methods have been proposed for this quantification. Rather than proposing a new uncertainty methodology, a contribution is made to the existing code scaling, applicability, and uncertainty (CSAU) method. A small-break loss-of-coolant accident with the break in the cold leg of a Westinghouse-type two-loop pressurized water reactor was selected for the analysis, and the CSAU methodology was used for uncertainty quantification. The uncertainty was quantified for the RELAP5/MOD3.2 thermal-hydraulic computer code. Some tools suggested by the uncertainty methodology based on accuracy extrapolation (UMAE) method were successfully applied to improve the CSAU methodology, particularly for nodalization qualification. A critical scenario with core uncovery was selected for the analysis, which showed that when uncertainty is added to the peak cladding temperature, the safety margin is sufficient. The tools developed by the UMAE method showed that the structure of the CSAU method is universal because it does not prescribe tools for the analysis.