Abstract : Ou4 is a recently discovered bipolar outflow with a projected size of more than one degree in the plane of the sky. It is apparently centred on the young stellar cluster -- whose most massive representative is the triple system HR 8119 -- inside the HII region Sh 2-129. The driving source, the nature, and the distance of Ou4 are not known. The basic properties of Ou4 and its environment are investigated in order to shed light on the origin of this remarkable outflow. Deep narrow-band imagery of the whole nebula at arcsecond resolution was obtained to study its detailed morphology. Long-slit spectroscopy of the tips of the bipolar lobes was secured to determine the gas ionization mechanism, physical conditions, and line-of-sight velocities. An estimate of the proper motions at the tip of the south lobe using archival plate images is attempted. The existing multi-wavelength data for Sh 2-129 and HR 8119 are also comprehensively reviewed. The observed morphology of Ou4, its emission-line spatial distribution, line flux ratios, and the kinematic modelling developed adopting a bow-shock parabolic geometry, illustrate the expansion of a shock-excited fast collimated outflow. The observed radial velocities of Ou4 and its reddening are consistent with those of Sh 2-129 and HR 8119. The improved determination of the distance to HR 8119 (composed of two B0 V and one B0.5 V stars) and Sh 2-129 is 712 pc. We identify in WISE images a 5 arcmin-radius (1 pc at the distance above) bubble of emission at 22 microns emitted by hot (107 K) dust grains, located inside the central part of Ou4 and corresponding to several [O III] emission features of Ou4. The apparent position of Ou4 and the properties studied in this work are consistent with the hypothesis that Ou4 is located inside the Sh 2-129 HII region, suggesting that it was launched some 90,000 yrs ago by HR 8119. The outflow total kinetic energy is estimated to be about 4E47 ergs. However, the alternate possibility that Ou4 is a bipolar planetary nebula, or the result of an eruptive event on a massive AGB or post--AGB star not yet identified, cannot be ruled out.