The Square Norm Algorithm is a modified version of the algorithm that finds fundamental units $K^\times$. In particular the aim of the algorithm is to find elements in the norm mapping $K^\times/K^{\times2} \to \mathbb{Q}^\times/\mathbb{Q}^{\times2}$. This is useful as the algorithm for finding Brauer Manin obstructions does not need the full fundamental unit group and only specifically needs these elements.