Context. The study of rotational velocity distributions for normal stars requires an accurate spectral characterization of the objects in order to avoid polluting the results with undetected binary or peculiar stars. This piece of information is a key issue in the understanding of the link between rotation and the presence of chemical peculiarities. Aims. A sample of 47 low v sin i A0-A1 stars (v sin i < 65km/s), initially selected as main-sequence normal stars, are investigated with high-resolution and high signal-to-noise spectroscopic data. The aim is to detect spectroscopic binaries and chemically peculiar stars, and eventually establish a list of confirmed normal stars. Methods. A detailed abundance analysis and spectral synthesis is performed to derive abundances for 14 chemical species. A hierarchical classification, taking measurement errors into account, is applied to the abundance space and splits the sample into two different groups, identified as the chemically peculiar stars and the normal stars. Results. We show that about one third of the sample is actually composed of spectroscopic binaries (12 double-lined and five single-lined spectroscopic binaries). The hierarchical classification breaks down the remaining sample into 13 chemically peculiar stars (or uncertain) and 17 normal stars.