To replace the present NAND flash memory, resistance switching random access memory (ReRAM), which has both memory and selection functionalities with a simple metal-insulator-metal structure should be implemented. To accomplish this goal, ReRAM must be self-rectifying, low-power-consuming, and highly uniform, and it must have reliable states. In this work, the Pt/TiO2/HfO2-x/TiN resistive switching memory structure showed self-rectifying resistive switching behavior with unprecedented unique I-V curves. This is named "self-current saturation," which can give an extremely uniform variation of the low resistance state. The plausible reasons for the whole switching behavior, including the unique I-V curves, in this material system are presented herein. The diffusion of Ti along the grain boundaries of HfO2 down to the bottom electrode TiN and the defect formation within the HfO2 layer near the TiO2/HfO2 interface made the resistance switching device have the characteristics of both the unidirectional diode and electronic bipolar switching devices.