As a procedure deriving UH (unit hydrograph), the root selection method necessitates only storm runoff data. However, this method must deal with the uncertainty related to the noise fluctuation of runoff ordinates and derive one optimal UH from many storms. This study proposes a procedure that applies the Savitzky-Golay filter to smooth the noise fluctuation of the runoff ordinates and uses the linear combination of UHs from individual storms to derive an optimal UH. The proposed method is applied to the storms of the Nenagh River basin in Ireland. The applicability of the Savitzky-Golay filter for smoothing the noise fluctuation of storm runoffs is examined by means of the Nash-Sutcliffe efficiency index. Furthermore, the root selection method is extended to also estimate IUHs. The results show that the adoption of the Savitzky-Golay filter improves the applicability of the root selection method and that the optimal UH predicts accurately the time-to-peak and peak discharge.