In the pipeline processing of Chandra data, a uniform random blur, currently defaulted to +/- 0.5 pixels, is added to the sky coordinate of ACIS data. Its primary objective is to remove artificial components which may be introduced by the aspect solution in this undersampled data and hence improve the PSF. However, one can also point out that the 0.5-pixel randomization will decrease the overall PSF simply because it degrades the original PSF. In our observations of the central region of M31 which consists of 7 separated ( ~ 5 ksec for each) pointings, we show that by removing pixel randomization, the spatial resolution is actually improved in the stacked deep image. Moreover, due to the improved PSF, the signal-to-noise ratio of faint sources is also increased. Therefore, for similar kinds of observations which consist of multiple short exposure pointings where spatial resolution becomes important, pixel randomization should be omitted, and the results should compare to those with randomization. In the meeting, we will present the results of our M31 observations obtained by the two methods and compare their differences.