  The paper treats a reaction-diffusion equation with hysteretic nonlinearity
on a one-dimensional lattice. It arises as a result of the spatial
discretization of the corresponding continuous model with so-called
nontransverse initial data and exhibits a propagating microstructure --- which
we call {\em rattling} --- in the hysteretic component of the solution. We
analyze this microstructure and determine the speed of its propagation
depending on the parameters of hysteresis and the nontransversality coefficient
in the initial data.
