We have systematically studied the effect of the orbital inclination in the outburst evolution of black hole transients. We have included all the systems observed by the Rossi X-ray timing explorer in which the thermal, accretion disc component becomes strongly dominant at some point of the outburst. Inclination is found to modify the shape of the tracks that these systems display in the colour/luminosity diagrams traditionally used for their study. Black hole transients seen at low inclination reach softer spectra and their accretion discs look cooler than those observed closer to edge-on. This difference can be naturally explained by considering inclination dependent relativistic effects on accretion discs. ; Comment: 8 pages, 4 figures, accepted for publication in MNRAS