Rigid-body docking of two molecules involves matching of their surfaces. A successful docking methodology considers two key issues: molecular surface representation, and matching. While approaches to the problem differ, they all employ certain surface geometric features. While surface normals are routinely created with molecular surfaces, their employment has surprisingly been almost completely overlooked. Here we show how the normals to the surface, at specific, well placed points, can play a critical role in molecular docking. If the points for which the normals are calculated represent faithfully and accurately the molecular surfaces, the normals can substantially ameliorate the efficiency of the docking in a number of ways. The normals can drastically reduce the combinatorial complexity of the receptor-ligand docking. Furthermore, they can serve as a powerful filter in screening for quality docked conformations. Below we show how deploying such a straight forward device, which is easy to calculate, large protein-protein molecules are docked with unparalleled short times and with a manageable number of potential solutions. Considering the facts that here we dock (1) two large protein molecules, including several large immunoglobulin-lysozyme complexes; (2) that we use the entire molecular surfaces, without a predefinition of the active sites, or of the epitopes, of neither the ligand nor the receptor; that (3) the docking is completely automated, without any labelling, or pre-specification, of the input structural database, and (4) with a single set of parameters, without any further tuning whatsoever, such results are highly desirable. This approach is specifically geared towards matching of the surfaces of large protein molecules and is not applicable to small molecule drugs.