We report the pulse dependent threshold voltage (V t ) variation of the Ovonic Threshold Switch (OTS) and its effect on the read window margin (RWM) in Cross-Point Memory (XPM). We found that OTS V t varies by the height and width of the write-current pulse. The varied V t is persistently maintained even after 2E4 cycling of the write pulse, which means that the phenomenon is not a temporary one, but a type of memory effect in OTS itself. Therefore, it would affect the overall V t window (AVt) of XPM by changing the Set V t (V t_Set ) and Reset V t (V t_Reset ) when combined with either phase-change memory (PCM) or resistive memory (RM). High-resolution transmission electron microscopy (HRTEM) and fast Fourier transform (FFT) images have proved that this phenomenon is not caused by the phase change of the OTS. Instead, a sub-threshold analysis extracted from the Poole-Frenkel model suggests that the phenomenon is associated with the variation of the amorphous network either by changes in the atomic bonding configuration or trap density.