We present an efficient and sensitive hybrid algorithm for local structure alignment of a pair of 3D protein structures. The hybrid algorithm employs both the URMS (unit-vector root mean squared) metric and the RMS metric. Our algorithm searches efficiently the transformation space using a fast screening protocol; initial transformations (rotations) are identified using the URMS algorithm. These rotations are then clustered and an RMS-based dynamic programming algorithm is invoked to find the maximal local similarities for representative rotations of the clusters. Statistical significance of the alignments is estimated using a model that accounts for both the score of the match and the RMS. We tested our algorithm over the SCOP classification of protein domains. Our algorithm performs very well; its main advantages are that (1) it combines the advantages of the RMS and the URMS metrics, (2) it searches extensively the transformation space, (3) it detects complex similarities and structural repeats, and (4) its results are symmetric. The software is available for download at biozon.org/ftp/software/urms/.