The atomic structure of a (2x2) reconstruction prepared on the 6H-SiC(000 (1) over bar) surface by annealing of an as-introduced or silicon-capped sample was determined. The structure is denoted (2x2)(C) to distinguish it from another (2x2)-periodic structure on the same surface. The reconstruction is characterized by a single silicon adatom per unit cell occupying a threefold-coordinated hollow site (H3). This result of the low-energy electron diffraction (LEED) analysis is consistent with scanning tunneling microscopy (STM) images showing one single protrusion per unit cell and a slightly silicon enriched stoichiometry with respect to bulk SiC as identified by Auger electron spectroscopy (AES). Furthermore, we found that this surface is preferably terminated by hexagonal stacking, i.e. on 60% of the surface the stacking switch characteristic for 6H-SiC is located below the first bilayer.