We suggest a new family of Co/Ni-based materials that may host unconventional high temperature superconductivity (high-Tc). These materials carry layered square lattices with each layer being formed by vertex-shared transition metal tetrahedra cation-anion complexes. The electronic physics in these materials is determined by the two dimensional layer and is fully attributed to the three near degenerated t2g d-orbitals close to a d 7 filling configuration in the d-shell of Co/Ni atoms . The electronic structure meets the necessary criteria for unconventional high Tc materials proposed recently by us to unify the two known high-Tc families, cuprates and iron-based superconductors. We predict that they host superconducting states with a d-wave pairing symmetry with Tc potentially higher than those of iron-based superconductors. These materials, if realized, can be a fertile new ground to study strongly correlated electronic physics and provide decisive evidence for superconducting pairing mechanism. PACS numbers: 75.85.+t, 75.10.Hk, 71.70.Ej, 71.15.Mb Successful theoretical predictions of high temperature superconducting materials rarely happen. The two known families of high T c materials, cuprates 1 and iron-based superconductors 2 , were discovered accidentally without any theoretical guide. Theoretical studies have been mainly devoted to explain rich phenomena observed in experiments. After almost three decades of intensive research, it has become extremely clear that if there is any chance to solve the elusive high T c mechanism, a successful theoretical prediction of new high T c materials is necessary.Recently, we suggest that a special electronic trait that separates the two high T c families from other correlated electronic materials is that in both high T c families, those d-orbitals that make the strongest in-plane d-p couplings in the cationanion complexes are isolated near Fermi surface energy [3][4][5] . In magnetically-driven superconducting mechanism, this property makes the effective antiferromagnetic(AFM) superexchange interactions to maximize their contribution to superconducting pairing and simultaneously reduces other unwanted side effects from other orbitals. We also further argued that this property can only be realized in very limited special cases 4 . Realizing such a property requires a strict symmetry match between local building blocks and global lattices, as well as a specific electron filling configuration in the dshells of transition metal atoms. In cuprates, which possess perovskite or perovskite-like structures, the speciality is only realized near the d 9 filling configuration in an octahedra (or square) complex to isolate the e g d x 2 −y 2 orbital near Fermi energy. In iron-based superconductors, it is only realized near the d 6 filling configuration of a tetrahedra complex to isolate two t 2g d xy -type orbitals 3,4 . Therefore, this speciality allows us to explain why high T c is such a rare phenomenon. It can be considered as a gene type character to guide us to search for ...