DyRh 4 B 4 has been known to crystallize in the primitive tetragonal (pt)-structure and to exhibit a ferromagnetic transition at 12K, the highest magnetic transition temperature in the entire series of the RRh 4 B 4 materials [For an extensive review on the magnetic and superconducting properties on the ternary superconductors, including RRh 4 B 4 , see, for example, Ø. Fischer, in: K.H.J. Buschow, E.P. Wohlfarth (Eds.), Ferromagnetic Materials, vol. 5, Elsevier Science Publishers B.V., 1990 (Chapter 6)]. We show here that our silicon-added samples of the nominal composition DyRh 4 B 4 Si 0.2 exhibit superconductivity below T c ∼4.5K and an antiferromagnetic transition below T N ∼2.7K. The 12K transition observed in the pt-DyRh 4 B 4 is completely suppressed. Our annealed samples mainly consist of domains of the chemical composition DyRh 3.9 B 4.2 Si 0.08 . 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-DyRh 4 B 4 phase and, therefore, coexist below T N ∼2.7K.