Existing linear methods for estimating homographies, rely on coordinate normalization, to reduce the error in the estimated homography. Unfortunately, the estimated homography depends on the choice of the normalization. The proposed extension to the (linear) Taubin estimator is the perfect substitute for such methods, as it does not rely on coordinate normalization, and produces homographies whose error is consistent with existing methods. Also, unlike existing linear methods, the proposed Taubin estimator is theoretically unbiased, and unaffected by similarity transformations of the correspondences in the two views. In addition, it can be adapted to estimate other quantities such as trifocal tensors.