  We introduce the Koenigs lattice, which is a new integrable reduction of the
quadrilateral lattice (discrete conjugate net) and provides natural integrable
discrete analogue of the Koenigs net. We construct the Darboux-type
transformations of the Koenigs lattice and we show permutability of
superpositions of such transformations, thus proving integrability of the
Koenigs lattice. We also investigate the geometry of the discrete Koenigs
transformation. In particular we characterize the Koenigs transformation in
terms of an involution determined by a congruence conjugate to the lattice.
