The purpose of the present work is to revisit the (1 X 2) reconstruction of the alpha-Fe2O3 ((1) over bar 012) surface, in order to answer the questions of composition and in-depth extension of the reconstructed layers, which still remained. We have thus studied by LEED (low energy electron diffraction) and AES (Auger electron spectroscopy) the modifications of the surface structure and composition as a function of different in situ (T, P-O2) treatments. The extension in depth of the (1 X 2) reconstruction increases with UHV annealing temperature (from 400 degrees C to 1000 degrees C, pot = 10(-10) mbar). Extending over several repeat units of the ((1) over bar 012) stacking sequence, the reconstructed layer reaches about 30 Angstrom depth after 900 degrees C annealing. A model of an ordered oxygen deficient layer in which one half of the octahedral iron sites is replaced by ordered tetrahedral ones, is proposed.