Binary regression models are essential for analyzing data where the outcome variable assumes one of two possible states. While traditional logistic and probit models rely on monotonic link functions, certain datasets exhibit non-monotonic relationships between predictors and binary outcomes, challenging the assumptions of these conventional methods. To address these challenges, this paper introduces a novel non-monotonic link function. The method's advantages are demonstrated through comparisons with traditional logistic regression, Cumulative Distribution Function Mixture Model (CDFMM) approach, and local logistic regression models on benchmark datasets, including Diabetes and Titanic datasets.