Finding structural similarities in distant proteins can reveal functional relationships that can not be identified using sequence comparison. Given two proteins A and B and threshold ε Å, we develop an algorithm, TRiplet-based Iterative ALignment (TRIAL) for computing the transformation of B that maximizes the number of aligned residues such that the root mean square distance of the alignment is at most ε Å. Our algorithm is designed with the specific goal of effectively handling proteins with low similarity in primary structure, where existing algorithms perform particularly poorly. Experiments show that our method outperforms existing methods. TRIAL alignment brings the secondary structures of distant proteins to similar orientations. It also finds more number of secondary structure matches at lower RMSD (Root Mean Square Deviation) values and increased overall alignment lengths. Its classification accuracy is up to 63% better than other methods, including CE and DALI. TRIAL successfully aligns 83% of the residues from the smaller protein in reasonable time while other methods align only 29 to 65% of the residues for the same set of proteins.