  DyRh4B4 has been known to crystallize in the primitive tetragonal
(pt)-structure and to exhibit a ferromagnetic transition at 12 K, the highest
magnetic transition temperature in the entire series of the RRh4B4 materials
[1]. We show here that our silicon-added samples of the nominal composition
DyRh4B4Si0.2 exhibit superconductivity below Tc ~ 4.5 K and an
antiferromagnetic transition below TN ~ 2.7 K. The 12 K transition observed in
the pt-DyRh4B4 is completely suppressed. Our annealed samples mainly consist of
domains of the chemical composition DyRh3.9B4.2Si0.08. These domains contain
two crystallographic phases belonging to the body-centred tetragonal
(bct)-structure and the orthorhombic (o)-structure. We have reasons to suggest
that superconductivity and antiferromagnetic ordering arise from bct- DyRh4B4
phase and, therefore, coexist below TN ~ 2.7 K.
