We propose and study a new type of double-layer holey structure with a wide bandgap. The structure can have glide symmetry in two orthogonal directions but not 2-D glide symmetry. We report results in terms of dispersion diagrams calculated with the eigensolver of a commercial solver, as well as with a multimode transfer matrix approach that permits an accurate calculation of the attenuation constant. The results demonstrate that the bandgap of the proposed structure can provide a wider fractional bandwidth and a larger attenuation constant than those of a 2-D glide-symmetric holey configuration. Therefore, this new type of periodic structure can be advantageous in preventing leakage in gap waveguide technology or, in general, parallel plate configurations and filters. The operation of this new unit cell is experimentally demonstrated with a double-flange configuration between 40-60 GHz.