  We construct a new discrete analog of the Dirac-K\"{a}hler equation in which
some key geometric aspects of the continuum counterpart are captured. We
describe a discrete Dirac-K\"{a}hler equation in the intrinsic notation as a
set of difference equations and prove several statements about its
decomposition into difference equations of Duffin type. We study an analog of
gauge transformations for the massless discrete Dirac-K\"{a}hler equations.
