A matching algorithm using surface complementarity between receptor and ligand protein molecules is outlined. The molecular surfaces are represented by “critical points,” describing holes and knobs. Holes (maxima of a shape function) are matched with knobs (minima). This simple and appealing surface representation has been previously described by Connolly [(1986) Biopolymers, Vol. 25, pp. 1229–1247]. However, attempts to implement this description in a docking scheme have been unsuccessful (e.g., Connolly, ibid.). In order to decrease the combinatorial complexity, and to make the execution time affordable, four critical hole/knob point matches were sought. This approach failed since some bound interfaces are relatively flat and do not possess four critical point matches. On the other hand, matchings of fewer critical points require a very time‐consuming, full conformational (grid) space search [Wang, (1991) Journal of Computational Chemistry, Vol. 12, pp. 746–750]. Here we show that despite the initial failure of this approach, with a simple and straightforward modification in the matching algorithm, this surface representation works well. Out of the 16 protein‐protein complexes we have tried, 15 were successfully docked, including two immunoglobulins. The entire molecular surfaces were considered, with absolutely no additional information regarding the binding sites. The whole process is completely automated, with no manual intervention, either in the input atomic coordinate data, or in the matching. We have been able to reach this level of performance with the hole/knob surface description by using pairs of critical points along with their surface normals in the calculation of the transformation matrix. The success of this approach suggests that future docking methods should use geometric docking as the first screening filter. As a geometrically based docking methodology predicts correct, along with incorrect, receptor‐ligand bound conformations, all solutions need to undergo energy screening to differentiate between them. © 1994 John Wiley & Sons, Inc.