In Wi-Fi fingerprint localization, a target sends its measured Received Signal Strength Indicator (RSSI) of access points (APs) to a server for its position estimation. Traditionally, the server estimates the target position by matching the RSSI with the fingerprints stored in database. Due to signal measurement uncertainty, this matching process often leads to a geographically dispersed set of reference points, resulting in unsatisfactory estimation accuracy. We propose a novel, efficient and highly accurate localization scheme termed Sectjunction which does not lead to a dispersed set of neighbors. For each selected AP, Sectjunction sectorizes its coverage area according to discrete signal levels, hence achieving robustness against measurement uncertainty. Based on the received AP RSSI, the target can then be mapped to the sector where it is likely to be. To further enhance its computational efficiency, Sectjunction partitions the site into multiple area clusters to narrow the search space. Through convex optimization, the target is localized based on the cluster and the junction of the sectors it is within. We have implemented Sectjunction, and our extensive experiments show that it significantly outperforms recent schemes with much lower estimation error.