The initial abstraction (Ia) versus maximum potential retention (S) relation in the Soil Conservation Service Curve Number (SCS-CN) methodology was revisited, and a new non-linear relation incorporating storm rainfall (P) and S was proposed and tested on a large set of storm rainfall-runoff events derived from the water database of United States Department of Agriculture-Agriculture Research Service (USDA-ARS). Employing root mean square error (RMSE), the performance of both the existing and proposed models was evaluated using the complete database, and for model calibration and validation, data were split into two groups: based on ordered rainfall (P-based) and runoff (Q-based). A specific formulation of the proposed model Ia=λS(P/(P+S))α with λ=0.3 and α=1.5 was found to generally perform better than the existing Ia=0.2S, and therefore was recommended for field applications. When evaluated using the observed Ia data, the proposed version performed significantly better than the existing one.