A new algorithm is reported which builds an alignment between two protein structures. The algorithm involves a combinatorial extension (CE) of an alignment path defined by aligned fragment pairs (AFPs) rather than the more conventional techniques using dynamic programming and Monte Carlo optimization. AFPs, as the name suggests, are pairs of fragments, one from each protein, which confer structure similarity. AFPs are based on local geometry, rather than global features such as orientation of secondary structures and overall topology. Combinations of AFPs that represent possible continuous alignment paths are selectively extended or discarded thereby leading to a single optimal alignment. The algorithm is fast and accurate in finding an optimal structure alignment and hence suitable for database scanning and detailed analysis of large protein families. The method has been tested and compared with results from Dali and VAST using a representative sample of similar structures. Several new structural similarities not detected by these other methods are reported. Specific one-on-one alignments and searches against all structures as found in the Protein Data Bank (PDB) can be performed via the Web at http://cl.sdsc.edu/ce.html.