Resistive RAM (RRAM) technologies are gaining importance due to their appealing characteristics, which include non-volatility, small form factor, low power consumption, and ability to perform logic operations in memory. These characteristics make RRAM highly suited for Internet of Things devices and similarly resource-constrained systems. This paper proposes a novel memristor-based xnor gate that enables the execution of xnor/xor function in the memristive crossbar memory. The proposed two-input xnor gate requires two steps to perform the xnor function. The design of the circuit utilizes bipolar and unipolar memristors and permits cascading by only adding an extra step and one computing memristor. To the best of our knowledge, this is the first native stateful xnor logic implementation. Spice simulations have been used to verify the functionality of the proposed circuit. This includes benchmarking the proposed design against the state-of-the-art stateful memristor-based logic circuits. The results for implementing three-input xor using the proposed circuit demonstrate efficient performance in terms of energy, latency, and area. The gate shows 56% saving in energy, 54% less number of steps (latency), and 50% less number of computing MR (area) compared with the state-of-the-art stateful xor/xnor implementations.