  The atomic and electronic structures of a graphene layer on top of the
$(2\times2)$ reconstruction of the SiC (000$\bar{1}$) surface are studied from
ab initio calculations. At variance with the (0001) face, no C bufferlayer is
found here. Si adatoms passivate the substrate surface so that the very first C
layer presents a linear dispersion characteristic of graphene. A small
graphene-substrate interaction remains in agreement with scanning tunneling
experiments (F.Hiebel et al. {\it Phys. Rev. B} {\bf 78} 153412 (2008)). The
stacking geometry has little influence on the interaction which explains the
rotational disorder observed on this face.
