We report a novel 3D structure-based method of predicting protein-protein interaction (PPI) partners. The method involves screening for pairs of tetrahedra representing interacting amino acids at the interface of the protein-protein (PP) complex. H-bonds and VDW interactions at the protein interface in the complex are determined, and interacting tetrahedral motifs (Reyes, V.M., 2008a) -- one from each protein -- representing backbone or side chain centroids of the interacting amino acids, are then built. Using the method, a collection of 801 functionally unannotated protein structures in the PDB were then screened for pairs of tetrahedral motifs characteristic of 9 binary complexes, namely: (1.) RAP-Gmppnp - c-RAF1 Ras-binding domain; (2.) RHOA - protein kinase PKN/PRK1 effector domain; (3.) RAC - RHOGD1; (4.) RAC - P67PHOX; (5.) kinase-associated phosphatase (KAP) - phospho-CDK2; (6.) Ig Fc - protein A fragment B; (7.) Ig light chain dimers; (8.) beta-catenin - HTCF-4; and (9.) IL-2 homodimers, of which the algorithm found 45, 192, 27, 48, 120, 0, 72, 90 and 276 putative complexes, respectively. Negative and positive controls test indicate that the screening algorithm has at least acceptable specificity and sensitivity. The results were further validated and narrowed down by applying the "Cutting Plane" and 'Tangent Sphere methods". (Reyes, V.M., 2008d) for quantitative determination of interface burial, which is indicative of monomer overlap in the complex. One advantage of our method besides its simplicity, speed and scalability, is its protein docking nature, a property that we demonstrate here.