High-resolution electron-microscopy (HREM) images from different hydroxyapatite (OHAp) samples showed p3 projection symmetry along [001] instead of the p6 projection symmetry compatible with the space group P6_3/m of OHAp. Image processing was used to establish without ambiguity that threefold symmetry dominates the images along [001]. OHAp crystals decompose in the transmission electron microscope and it is concluded that the threefold symmetry observed corresponds to an early step in the decomposition process, the dehydration of OHAp to oxyapatite (OAp). A structural model for OAp where every second O atom along the 6(3) axis in OHAp is removed has the maximal space-group symmetry P{\bar 6}. This is compatible with the p3 projection symmetry observed. Atomic shifts in this OAp model compared to the OHAp structure were estimated using the HREM images and geometric optimizations of the atomic structure. No refinements of the atomic coordinates against diffraction data were possible but the simulated HREM images of this crude model fit well with the experimental images.