We analysed all archival Rossi X-ray Timing Explorer (RXTE) observations of the neutron star low-mass X-ray binary 4U 1636−53 up to 2010 May. In 528 out of 1280 observations we detected kilohertz quasi-periodic oscillations (kHz QPOs), with ∼65 per cent of these detections corresponding to the so-called lower kHz QPO. Using this QPO we measured, for the first time, the rate at which the QPO frequency changes as a function of QPO frequency. For this we used the spread of the QPO frequency over groups of 10 consecutive measurements, sampling time-scales between 320 and 1600 s and the time derivative of the QPO frequency, , over time-scales of 32–160 s. We found that (i) both the QPO-frequency spread and decrease by a factor of ∼3 as the QPO frequency increases. (ii) The average value of decreases by a factor of ∼2 as the time-scale over which the derivative is measured increases from less than 64 to 160 s. (iii) The relation between the absolute value of and the QPO frequency is consistent with being the same both for the positive and negative QPO-frequency derivatives. We show that, if either the lower or the upper kHz QPO reflects the Keplerian frequency at the inner edge of the accretion disc, these results support a scenario in which the inner part of the accretion disc is truncated at a radius that is set by the combined effect of viscosity and radiation drag.