The current consensus is that only one type of horn, the ossicone, exists in the giraffe and that the central or median horn is both structurally and developmentally similar to the paired parietal horns. We have shown that the paired ossicones are composites of three structures: an innermost large frontoparietal boss base, the ossicone, and outermost layers of secondary bone growth. The median hom, to which we assign the name ‘giraffacone’, is a composite of only two structures: the median frontonasal boss and the overlying secondary bone growth. In older males, secondary bone growth due to combat clashes covers the entire calvaria. In females, there is little or no such secondary bone growth over the ossicones and the rest of the skull roof. Consequently, the median horn consists only of the frontal boss. The shape of the ossicones without the secondary bone layer, as revealed in young males and females, is herein described. It is shown how a distinction can be made between the variation in shape due to secondary bone growth and the variation of the ossicone. It is apparent that ossicone shape is not as variable as previously thought. We found secondary bone growth in the horns of Palaeomeryx and in the ossicones of Giraffinae, Giraffokeryx punjabiensis, Samotherium africanum and Sivatheriinae.