Very thin iron columnar layers have been obliquely grown on glass under ultra-high vacuum, and studied by cross-sectional transmission electron microscopy, selected-area electron diffraction and X-ray texture analysis experiments. Micrographs of layers a few tens of nanometres thick have been obtained. For the first time, we put forward the existence of an oblique growth for such thin layers in the case of metals. We discuss the influence of the inclination of the flux, and we compare our results with existing theoretical models. We also describe the influence of other parameters such as the substrate temperature or the divergence of the incident flux. We finally attempt to explain this columnar morphology by means of a Volmer-Weber growth and a shadowing effect.