  We present a microscopic treatment of edge magnetoplasmons (EMP's) within the
random-phase approximation for strong magnetic fields, low temperatures, and
filling factor $\nu =1(2)$, when a weak short-period superlattice potential is
imposed along the Hall bar. The modulation potential modifies both the spatial
structure and the dispersion relation of the fundamental EMP and leads to the
appearance of a novel gapless mode of the fundamental EMP. For sufficiently
weak modulation strengths the phase velocity of this novel mode is almost the
same as the group velocity of the edge states but it should be quite smaller
for stronger modulation. We discuss in detail the spatial structure of the
charge density of the renormalized and the novel fundamental EMP's.
