We present a 90 per cent flux-complete sample of the 201 X-ray-brightest clusters of galaxies in the northern hemisphere (δ ≥ 0°), at high Galactic latitudes (ǀbǀ ≥ 20°), with measured redshifts z ≤ 0.3 and fluxes higher than 4.4 × 10−12 erg cm−2 s−1 in the 0.1–2.4 keV band. The sample, called the ROSAT Brightest Cluster Sample (BCS), is selected from ROSAT All-Sky Survey data and is the largest X-ray-selected cluster sample compiled to date. In addition to Abell clusters, which form the bulk of the sample, the BCS also contains the X-ray-brightest Zwicky clusters and other clusters selected from their X-ray properties alone. Effort has been made to ensure the highest possible completeness of the sample and the smallest possible contamination by non-cluster X-ray sources. X-ray fluxes are computed using an algorithm tailored for the detection and characterization of X-ray emission from galaxy clusters. These fluxes are accurate to better than 15 per cent (mean 1σ error).