Skin zones with distinct hydraulic properties often form around wellbores during drilling operations. Conventional skin-factor models, developed for low-permeability (positive) skin, assume discontinuous hydraulic heads between the wellbore and aquifer. However, these models may be inadequate for high-permeability (negative) skin scenarios resulting from intensive well development. This study derives a new skin-factor approach for negative skin approaches based on the two-zone model approach. We derive a new skin-factor approach that maintains continuous heads between the wellbore and aquifer while allowing for discontinuous fluxes. Using Laplace and finite cos-Fourier transformations, we develop a groundwater flow model for aquifer pumping under a partially penetrating well, incorporating this new approach. An asymptotic expansion method is employed to obtain a large-time solution. The proposed model is also compared to the existing two-zone model. Sensitivity analysis reveals that high-permeability skin significantly affects drawdown, particularly when there is a sudden increase in porosity within the skin zone. This revised approach provides a more accurate framework for modeling various skin effects, offering valuable insights for groundwater management and well hydraulic modeling in both hydrogeology and petroleum engineering applications.