Effect of climate change and catchment change on the long-term water balance is of considerable interest at a range of spatial scales. The total differential of runoff within the Budyko framework, which has been widely used to attribute the change in runoff to the effect of climate and catchment changes, is not precise in which there is always some residual between the observed and estimated change in runoff. The objective of this study is to propose and evaluate a new partition method based on the Budyko complementary relationship for runoff. Algebraic identities have ensured that the change in runoff can be decomposed into two components precisely without any residuals using this complementary method. In addition, the complementary method allows estimation of the upper and lower bounds of the climate effect and catchment effect. The new method was compared with the total differential method and an extrapolation method for 15 catchments in Australia. Results show that the average range of the catchment effect using the complementary method was 6.7 mm for 14 of the 15 catchments, which is much smaller than that estimated with the total differential method (51.5 mm). The average of the upper and lower bounds was shown to be in good agreement with the effect of climate and catchment changes estimated using the extrapolation method (R2 = 0.98 for both). Correlation analysis indicates that the average of these bounds is the best estimate of the magnitude of the climate and catchment effect for the 15 catchments examined.