This article introduces a novel protein structure alignment method (named TALI) based on the protein backbone torsion angle instead of the more traditional distance matrix. Because the structural alignment of the two proteins is based on the comparison of two sequences of numbers (backbone torsion angles), we can take advantage of a large number of well-developed methods such as Smith-Waterman or Needleman-Wunsch. Here we report the result of TALI in comparison to other structure alignment methods such as DALI, CE, and SSM ass well as sequence alignment based on PSI-BLAST. TALI demonstrated great success over all other methods in application to challenging proteins. TALI was more successful in recognizing remote structural homology. TALI also demonstrated an ability to identify structural homology between two proteins where the structural difference was due to a rotation of internal domains by nearly 180$^circ$.