Optical identifications of a few thousands of IRAS sources showed that IRAS Point Source and IRAS Faint Source catalogues (PSC and FSC, respectively) contain many quasars and active galactic nuclei, late-type stars, planetary nebulae, variables, etc. To increase the efficiency of using IRAS PSC and FSC, which contain a lot of common sources, one needs a joint catalogue of all IRAS point sources with improved data based on both catalogues. However, cross-correlation of the catalogues is not so easy, as the association of many sources is relative, and not always it is obvious, whose source from one catalogue corresponds to the other one in the second catalogue. This problem exists in case of using standard cross-correlation tools. Therefore, we have created a tool for cross-matching astronomical catalogues and we have applied it to IRAS PSC and FSC. Using this tool we have carried out identifications with a search radius corresponding to 3-{sigma} of errors for each source individually rather than a standard radius for all sources. As a result, we obtained 73,770 associations. In addition, we have made cross-correlations with AKARI-IRC, AKARI-FIS and WISE catalogues. We created a catalogue of 345,163 IRAS sources with high positional accuracy and with 17 photometric measurements from 1.25 to 160 ?m range, providing a detailed catalogue for IRAS point sources.