International audienceWe studied X-ray reverberation lags in the Black hole X-ray binary (BHXRB) GX 339–4 at the end of the 2014–2015 outburst. We analysed data from an XMM–Newton campaign covering the end of the transition from the soft to hard state, and the decrease of luminosity in the hard state. During all the observations we detected, at high frequencies, significant disc variability, responding to variations of the power-law emission with an average time delay of ∼0.009 ± 0.002 s. These new detections of disc thermal reverberation add to those previously obtained and suggest the lag to be always present in hard and hard-intermediate states. Our study reveals a net decrease of lag amplitude as a function of luminosity. We ascribe thi...