<p>We present a novel least-squares algorithm for fitting ellipses to scattered data, addressing the numerical instabilities of traditional direct methods. The proposed approach achieves significant computational efficiency while providing robust and reliable results. Its closed-form nature ensures fixed computation time, making it well-suited for real-time machine vision applications. Performance is evaluated against both the original formulation and a recent improvement across a range of ellipse configurations, demonstrating superior accuracy and stability. Finally, the performance of the proposed algorithm is evaluated against both the original formulation and a recent improvement across various ellipse configurations.</p>