We have measured radial velocities for 53 B-type stars, between B1 and B9, in the young open cluster NGC 6231 through a cross-correlation technique with synthetic spectra. Two measurements for 36 stars of the sample were obtained with a time separation of about two years. We derived a minimum binary fraction of 52% in the considered population. The velocity determination precisions were simulated and we analysed their dependence upon the S/N ratios of the spectra and upon the stellar rotational velocities. We discuss the selection of the templates for the correlation.