Abstract: A sample of the brightest point-like sources observed with the ROSAT-HRI were analysed to asses on the intrinsic shape of the ROSAT-HRI Point Spread Function (PSF). Almost all of the HRI observations collected during the ROSAT lifetime are found to be artificially broadened by factors up two ~2 due to residual errors in the ROSAT aspect solution. After correction by departing pointing positions, the width of the core of the PSF is found to be less than 5 arcsec (half energy width, HEW). On the basis of these results, an improved analytical representation of the ROSAT-HRI PSF is provided. However, for most of the new observations the source countrate is too weak to allow reliable recovering pf the ROSAT-HRI resolution. Therefore, a series of examples (data, correction, and theoretical PSF) are given in order to help the ROSAT user in determining whether "his/her source" is extended or not.