The monotypic genus Paraschizopera Wells, 1981 (ex Diosaccidae) is transferred to the Tetragonicipitidae on the basis of segmentation of antennary exopod and P2-P4 endopods, setation of P1 and overall similarity in mouthpart structure. Paraschizopera is the most primitive genus of the family and closely related to Diagoniceps Willey, 1930 which is redefined to encompass only the laevis-group. The menaiensis-group is allocated to Paraschizopera which includes now P. beckeri Wells (type-species), P. menaiensis (Geddes) and P. trifida (Yeatman). The new name D. brevicauda is proposed for Diagoniceps sp. sensu Bodin (1979). Keys are provided to the species of Paraschizopera and Diagoniceps, and to the genera of the Tetragonicipitidae.