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The exotic physics revealed in geometrically frustrated materials has led to a search for families of geometrically frustrated systems which may be systematically studied. Familiar frustrated systems include the Kagome, pyrochlore, spinel, stacked trianguler, and face-centered cubic systems. Less well-known are the so-called "rock salt ordered" A₅BO₆ systems, particularly with high-Z magnetic ions exhibiting strong spin-orbit coupling on the B site. These systems tend to crystallize in either monoclinic (C2/m) or orthorhombic (Fddd) crystal settings, with somewhat different exchange parameters in each case, and these systems exhibit a wide range of ground states ranging from commensurate antiferromagnetism to spin-glass behavior. Li₄MgReO₆ had been previously synthesized in the monoclinic space group, exhibiting AFM order at 12K. Here we report synthesis of Li₄MgReO₆ in the orthorhombic space group, and characterization using magnetic susceptibility and muon spin relaxation, finding AFM order setting in below 2K.