Physically Unclonable Functions (PUFs) are emerging cryptographic primitives used to implement low-cost device authentication and secure secret key generation. While several solutions exist for classical CMOS devices, novel proposals have been recently presented which exploit emerging technologies like magnetic memories. The Spin-Transfer-Torque Magnetic Random Access Memory (STT-MRAM) is a promising choice for future PUFs due to the high variability affecting the electrical resistance of the Magnetic Tunnel Junction (MTJ) device in anti-parallel magnetization. Some papers showed that these devices could guarantee high levels of both unclonability and reliability. However, 100% reliability is not yet obtained in those proposals. In this paper we present an effective method to identify the unreliable cells in a PUF implementation. This information is then used to create a zero bit-error-rate PUF scheme.