Point Cloud Registration is a key step in tasks like Simultaneous Localization and Mapping and 3D Reconstruction. Methods that manage to use geometric information efficiently, show remarkable registration results in practice. Although these methods, in general, introduce intricate cost functions that prove challenging for general-purpose optimization algorithms. In this work, we introduce an efficient algorithm for solving the Generalized Least Squares problem, involved in the Generalized Iterative Closest Point, the most representative method of this class. Our method successfully combines the speed of the fastest algorithms with the accuracy of the most precise.