This study presents a generalized form of the General Emrem Distribution with a Scale Parameter (GMSED). The proposed generalization aims to extend the flexibility of the original model and broaden its potential for statistical modelling. The mathematical formulation of the generalized distribution is established, and its principal statistical properties are derived analytically. These properties include: moments, quantiles, moment generating function, survival function, and hazard rate function. The derived results provide a comprehensive mathematical characterization of the proposed distribution and establish a foundation for further theoretical investigation and potential statistical applications. The study contributes to the literature on generalized probability distributions by extending an existing model and systematically examining its mathematical properties.