It is now established that thermal disc emission and non-thermal jet emission can both play a role at optical/infrared (OIR) wavelengths in X-ray transients. The spectra of the jet and disc components differ, as do their dependence on mass accretion properties. Here we demonstrate that the OIR colour-magnitude diagrams (CMDs) of the evolution of the X-ray transient XTE J1550-564 in outburst can be used to separate the disc from the jet. Monitoring in two wavebands is all that is required. This outburst in 2000 was well studied, and both disc and jet were known to contribute. During the outburst the data follow a well-defined path in the CMD, describing what would be expected from a heated single-temperature blackbody of approximately constant area, except when the data appear redder than this track. This is due to the non-thermal jet component which dominates the OIR moreso during hard X-ray states at high luminosities, and which is quenched in the soft state. The CMD therefore shows state-dependent hysteresis, in analogy with (but not identical to) the well-established X-ray hardness-intensity diagram of black hole transients. The blackbody originates in the X-ray illuminated, likely unwarped, outer accretion disc. We show that the CMD can be approximately reproduced by a model that assumes various correlations between X-ray, OIR disc and OIR jet fluxes. We find evidence for the OIR jet emission to be decoupled from the disc near the peak of the hard state.