Crystalline terbium–iron compounds generate large magnetostrictive strains but for practical application require relatively large fields to overcome magnetocrystalline anisotropy. Their amorphous counterparts are magnetically softer and yet potentially useful magnetostrictive strains are still exhibited due to the presence of the Tb ions. As part of our investigation into the origins and magnitudes of the magnetostriction in amorphous rare earth–iron alloys, their magnetic properties have been subjected to close examination. Melt-spun ribbons of TbFe2 containing between 3 and 14 at. % boron were prepared and shown to be amorphous (>6 at. % B). The field and temperature dependences of magnetization have been measured in the region 4.5 K<T<300 K with fields up to 5 T using a superconducting quantum interference device magnetometer. The temperature dependences of coercivity and remanence have been determined. Zero field and field cooled magnetization curves indicate a spin freezing temperature ∼240 K. Analyzing the demagnetization curves in terms of the random anisotropy model proposed by Harris, Plischke, and Zuckermann (HPZ) [R. Harris, M. Plischke, and M. J. Zuckermann, Phys. Rev. Lett. 31, 160 (1974)] shows that the anisotropy and exchange energy in (TbFe2)1−xBx are of comparable magnitudes. Coupled with the sharp decrease of the anisotropy with increasing temperature this leads to an interesting thermal behavior of the remanence with a local minimum at ∼140 K. Different concentrations of boron seem to have no significant effect on the magnetic properties. Boron acts purely as a “glass former” necessary for producing amorphous TbFe2 by rapid cooling.