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Current wireless sensor network localization algorithms are categorized either as range-free or range-aware algorithms based on whether they use the range (i.e., distance) information. Although wireless sensor systems usually have available received signal strength (RSS) readings, this useful information has not been effectively used in the existing localization algorithms. The existing range-free algorithms do not use this information, and the range-aware algorithms require sophisticated range techniques to estimate ranges. In this paper, we introduce and develop a partial-range-aware localization scheme utilizing RSS readings. The scheme can be implemented in a distributed way and can be used in any hop-based range-free algorithms to improve their localization accuracy. Through extensive simulation, the results show that the partial-range-aware algorithm can improve the localization accuracy by reducing position errors up to 50% of the previous range-free localization results.