<p>Numerous fourth-order iterative methods have been proposed for solving scalar nonlinear equations, with optimal-order schemes receiving particular attention due to their computational efficiency. However, many of these methods face practical limitations, such as reduced accuracy, slow convergence, failure to maintain the theoretical order of convergence in certain situations, and an inability to be extended to multi-dimensional problems. This paper addresses these challenges by introducing a novel family of two-step methods, with the classical Newton’s method serving as the first step. The proposed approach achieves fourth-order convergence using only three function evaluations per iteration, thereby satisfying the optimality condition of the Kung–Traub conjecture. Notably, several well-known fourth-order methods emerge as special cases of this family. Numerical experiments and visualizations of the basins of convergence are presented to evaluate the performance. The results demonstrate that the new scheme provides superior accuracy and larger convergence regions compared to existing fourth-order methods.</p>