Anchorless localization, in which nodes in a wireless network are located without the use of reference nodes, is valuable for applications such as public safety where rapid setup is required. The distances between nodes form a Euclidean distance matrix (EDM), and as distance is not directly measured between all pairs of nodes the EDM needs to be completed by inferring the unknown values. Manifold flattening (MF) is a recently presented technique for EDM completion which has been shown to be effective for anchorless localization. In the bottom-up process of EDM completion, increasingly larger streams of pair values are generated for inferring the missing ranges. In this paper we present a new algorithm for filtering the data streams that leads to an EDM completion algorithm with reduced error compared to the original MF algorithm. Through simulation we demonstrate that this leads to improved performance for anchorless localization.