We have recently developed a fast approach to comparisons of 3-dimensional structures. Our method is unique, treating protein structures as collections of unconnected points (atoms) in space. It is completely independent of the amino acid sequence order. It is unconstrained by insertions, deletions, and chain directionality. It matches single, isolated amino acids between 2 different structures strictly by their spatial positioning regardless of their relative sequential position in the amino acid chain. It automatically detects a recurring 3D motif in protein molecules. No predefinition of the motif is required. The motif can be either in the interior of the proteins or on their surfaces. In this work, we describe an enhancement over our previously developed technique, which considerably reduces the complexity of the algorithm. This results in an extremely fast technique. A typical pairwise comparison of 2 protein molecules requires less than 3 s on a workstation. We have scanned the structural database with dozens of probes, successfully detecting structures that are similar to the probe. To illustrate the power of this method, we compare the structure of a trypsin-like serine protease against the structural database. Besides detecting homologous trypsin-like proteases, we automatically obtain 3D, sequence order-independent, active-site similarities with subtilisin-like and sulfhydryl proteases. These similarities equivalence isolated residues, not conserving the linear order of the amino acids in the chains. The active-site similarities are well known and have been detected by manually inspecting the structures in a time-consuming, laborious procedure. This is the first time such equivalences are obtained automatically from the comparison of full structures. The far-reaching advantages and the implications of our novel algorithm to studies of protein folding, to evolution, and to searches for pharmacophoric patterns are discussed.