Memristors have proven to be powerful analogs of neural synapses. While there have been some efforts to exploit this feature, the intrinsic analog nature of the memristive element has not been fully utilized. This paper presents a hardware-efficient neuromorphic CMOS-memristor pattern classifier. The system takes advantage of the memristor as a true analog memory, and Spike Timing Dependent Plasticity (STDP) is utilized to program memristors in a recurrent neural network. System co-simulations are performed in Verilog-AMS with CMOS devices and previously published memristive models. The results indicate the power of this approach in pattern classification using unsupervised learning.