The magnetic Ln 3+ ions in the fergusonite and scheelite crystal structures form a truncated hyperhoneycomb net that can be labelled as H −1 by analogy with the harmonic honeycomb series H N [Modic et al., Nat. Commun. 5, 4203 (2014)]. This H −1 magnetic lattice is an elongated form of the diamond lattice and is therefore predicted to host exotic magnetic ground states. In this study, polycrystalline samples of the fergusonite orthotantalates M -LnTaO4 (Ln = Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er) are synthesized and then characterized using powder diffraction and bulk magnetometry and heat capacity. TbTaO 4 orders antiferromagnetically at 2.25 K into a commensurate magnetic cell with k = 0, magnetic space group 14.77 (P 21 /c) and Tb moments parallel to the a-axis. No magnetic order was observed in the other materials studied, leaving open the possibility of exotic magnetic states at T < 2 K.