The ac electrical resistance, heat capacity, static magnetic susceptibility, thermal conductivity, and linear thermal expansion coefficient have been measured for the superconducting ternary compound TmRh4B~. The results indicate that the Tm 3 § magnetic moments order at about 0.4 K, while bulk superconductivity, which occurs at 9.8K, persists to temperatures below 60 inK, which was the low-temperature limit of the apparatus. Various possibilities for the type of magnetic order are examined.