Eliminating redundant or non-informative access points (APs) in an indoor positioning system not only reduces the computational cost of fingerprinting but also can improve the positioning accuracy. In this paper, we propose a dimensionality reduction technique to restrict the location fingerprints to only signal strength values received from informative APs. We argue that the most informative APs for the positioning system are those which provide unique signal strength values that enhance the regional discrimination. Therefore, we propose a different implementation of the fast orthogonal search (FOS) method to quantify the uniqueness of the received signal strength (RSS) values measured from each AP at each location point. To assess the proposed method, two important factors were taken into consideration; the amount of achieved reduction and the resulting positioning accuracy. Real RSS data was used in our experiments, and the results show that the proposed modification results in a better positioning performance than the original FOS implementation, especially for significant reductions.