In order to identify peculiar X-ray sources, we select 442 sources with no counterparts in other wavelength bands (as of the year 1999) from the ROSAT All-Sky Survey Bright Source Catalog. We cross- correlate this initial list with the NASA/IPAC Extragalactic Database, the USNO and WISE catalogs, and the HEASARC XRAY Master Catalog. Eventually, we are left with four unidentified sources with no counterparts in other wavelength bands. We present these four sources and their X-ray properties in this paper.