The disc of galaxies is made of the superposition of a thin and a thick disc. Star formation is hosted in the thin discs and contributes to their growth. Thick discs are formed of old stars. The formation mechanisms of thick discs are under discussion. Thick discs might have formed either at high redshift on a short timescale or might have been built slowly over a Hubble-Lemaitre time. They may have an internal or an external origin. Here we adopt a galactic archaeology approach to study the thick disc of ESO 533-4, i.e. we study the kinematics and the stellar populations of this galaxy in detail. ESO 533-4 is a Southern, nearby, and almost bulgeless galaxy. We present the first ever Integral Field Unit spectroscopy of an edge-on galaxy with enough depth and quality to study the thick disc. We exposed ESO 533-4 with the blue grism of the VIMOS instrument of the VLT for 6.5 h. The field of view covered an axial extent from similar to 0.1 r(25) to similar to 0.7 r(25), where r(25) is the 25 mag arcsec(-2) isophotal radius. This corresponds to the range from similar to 1 kpc to similar to 7 kpc. We used pPXF and the MILES library to obtain velocity and stellar population maps. We compared our kinematic data with simple GADGET-2 models. The apparent rotational lag of the thick disc of ESO 533-4 is compatible with that expected from the combinations of two effects: differential asymmetric drift and the projection effects arising from studying a disc a few degrees (2-3 degrees) away from edge-on. Thus, ESO 533-4 contains little or no counter-rotating material. This is compatible with three formation scenarios: the secular dynamical heating of an initially thin disc, the formation of the thick disc at high redshift in an early turbulent disc phase, and the creation of a thick disc in a major merger event. If this last mechanism occurred in all galaxies, it would cause retrograde thick discs in half of them. These retrograde discs have not been observed in the five massive disc galaxies (circular velocity v(c) greater than or similar to 120 km s(-1)) for which the kinematics of the thick disc is known. The stellar populations map indicates that the populations of the thin and the thick discs of ESO 533-4 are possibly separated in the Age-log (Z/Z(circle dot)) plane. This would imply that thin and thick discs are formed of two distinct stellar populations. The stellar population results are not fully conclusive because of the high dust extinction in ESO 533-4 and because recovering stellar populations is a difficult inverse problem. Having said that, the stellar population results do not favour a secular evolution origin for the thick disc. Hence, we suggest that the thick disc of ESO 533-4 formed in a relatively short event.