  The formation mechanisms of thick discs are under discussion. Thick discs
might have formed either at high redshift on a short time-scale or might have
been built slowly over time. They may have an internal or an external origin.
Here we study in detail the kinematics and the stellar populations of the thick
disc of ESO533-4. ESO533-4 is a nearby bulgeless galaxy.
  We present the first ever IFU study of an edge-on galaxy with enough depth to
study the thick disc. We exposed ESO533-4 with VIMOS@VLT for 6.5hours. The FOV
covered an axial extent 0.1-0.7r_25 (1-7kpc). 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 ESO533-4 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) away from edge-on. Thus, ESO533-4 contains little or no retrograde
material. This is compatible with three formation scenarii: the secular heating
of an initially thin disc, the formation of the thick disc at high redshift in
a turbulent disc phase, and its creation in a major merger event. If happening
in all galaxies, this last mechanism would cause retrograde thick discs in half
of them. Retrograde discs have not been observed in the five massive disc
galaxies (v_c>120km s^-1) for which thick disc kinematics are known. The
populations of the thin and the thick discs are separated in the
Age-log(Z/Z_Sun) plane. Thus, the thin and thick discs are made of two distinct
stellar populations. Although the stellar population results are not conclusive
due to the high dust extinction in ESO533-4, they do not favour a secular
evolution origin for the thick disc. Hence, we suggest that the thick disc of
ESO533-4 formed in a relatively short event (Abridged).
