We have investigated the short-term linear relation between the rms variability and the flux in 1961 observations of nine black hole X-ray binaries. The rms–flux relation for the 1–10 Hz range is ubiquitously observed in any observation with good variability signal-to-noise ratio (>3 per cent, 1–10 Hz fractional rms). This concurs with results from a previous study of Cygnus X-1, and extends detection of the rms–flux relation to a wider range of states. We find a strong dependence of the flux intercept of the rms–flux relation on source state; as the source transitions from the hard state into the hard intermediate state, the intercept becomes strongly positive. We find little evidence for flux dependence of the broad-band noise within the power spectra shape, excepting a small subset of observations from one object in an anomalous soft state. We speculate that the ubiquitous linear rms–flux relation in the broad-band noise of this sample, representing a range of different states and objects, indicates that its formation mechanism is an essential property of the luminous accretion flow around black holes.