A double anisotropic coherent backscattering cone was found. In contrast to the (single) anisotropic coherent backscattering, which was observed in liquid crystals, here, the long axis of the elongated structures changes its orientation with angular distance. We compared our results with the two-dimensional Fourier transform of spatially resolved reflectance measurements and found good agreement, which is predicted by the reciprocity thesis. Furthermore, a Monte Carlo model was applied to reproduce successfully the results of the experiment, whereas the double anisotropy is not predicted by diffusion models.