We present highly stable bilayer HfO2/TiO2 memristive synapse for neuromorphic computing applications. The memristive synapse shows repetitive 220 Long-term potentiation and depression cycles without any breakdown with total number of 220k pulses. The nonlinear values of potentiation and depression are 2.52 and -2.63, respectively with 1000 conductance pulses (500 pulses of potentiation and 500 pulses of depression). The experimental data of potentiation and depression was used to train HNN for pattern recognition of 28×28 pixels comprising 784 synapses. In 16 iterations, the HNN can be successfully trained to identify the input image with a training accuracy of about 97%. Moreover, the device has good retention (104 s) at 120 °C. These excellent synaptic characteristics of annealed device allows it for artificial intelligence systems in near future.