The absolute orientation technique, minimizing the mean squared error between two matched point sets under similarity transformations, has numerously applied in the areas of photogrammetry, robotics, object motion analysis as well as object pose estimation following recognition. Based on it, in this paper, a total least squares fitting algorithm, which generates a fixed point set from k corresponding original point sets and minimizes the mean squared error between the fixed point sets and these k point sets, is proposed and proved. Experiments and interesting applications are also presented to show its efficiency, accuracy and robustness.