Position verification problem is an important building block for a large subset of wireless sensor networks (WSN) applications. As a result, the performance of the WSN degrades significantly when misbehaving nodes report false location information in order to fake their actual position. In this paper we propose the first deterministic distributed protocol for accurate identification of faking sensors in a WSN. Our scheme does not rely on a subset of trusted nodes that cooperate and are not allowed to misbehave. Thus, any subset of nodes is allowed to try faking its position. As in previous approaches, our protocol is based on distance evaluation techniques developed for WSN. On the positive side, we show that when the received signal strength (RSS) technique is used, our protocol handles at most $\lfloor\frac{n}{2}\rfloor-2$ faking sensors. When the time of flight (ToF) technique is used, our protocol manages at most $\lfloor\frac{n}{2}\rfloor-3$ misbehaving sensors. On the negative side, we prove that no deterministic protocol can identify faking sensors if their number is $\lceil\frac{n}{2}\rceil-1$ . Thus, our scheme is almost optimal with respect to the number of faking sensors. We discuss application of our technique in the trusted sensor model. More specifically, our results can be used to minimize the number of trusted sensors that are needed to defeat faking ones.