We present the colour indices V-R of BL Lacertae object PKS 0537-441 on the basis of the photometric data monitored by the Rapid Eye Mounting (REM) telescope located at the ESO Cerro La Silla observatory (Chile). Nearly 700 quasi-simultaneous data groups were collected during the period from 2004 to 2010. Our colour analysis shows the existence of at least two variability mechanisms: one is the long-term chromatic mechanism in which the variation traces a 0.04+/-0.01 slope in the V-R versus V plot, the other is the chromatic mechanism implying the spectral changes during the flares and on intraday time-scales. A general bluer-when-brighter trend is confirmed in both ascent and descent states during the flares and in the 2010 February flare interval, while a much stronger bluer-when-brighter chromatism is observed in both faint and bright states on intraday time-scales. The discrete correlation function analysis reveals the existence of a time-lag of 13^+5.8^-1.2 d between colour indices and magnitudes during the period MJD 54404-54453, whereas no measurable time-lag during other periods is found. Our results suggest that geometric effects may be responsible for the long-term achromatic mechanism, while the intrinsic shock-in-jet mechanism may produce the chromatic variability during the flares and on intraday time-scales.