Hemerythrin is not, as the name might suggest, a heme. The "heme" was at first applied to any oxygen-carrying proteins, such as hemoglobin, and when hemoglobin was analyzed, the heme structure was named for the iron-porphyrin cofactor in the transport protein (globin being a general term for a globular protein). Later, after hemerythrin was named, it was discovered that not every oxygen-carrying protein has a heme prosthetic group.
As it turns out the oxygen binding site is a binuclear iron center, the irons connect through a μ-oxo bridge. The irons themselves are coordinated to the protein through the carboxylate side chains of a glutamate and aspartate group, and five histidines.