We have developed a feedback algorithm for protein structure alignment that uses a series of phases to improve the global alignment between two protein backbones. The method implements a self-improving learning strategy by sending the output of one phase, the global alignment, to the next phase as an input. A web portal implementing this method has been constructed and is freely available for use at http://fpsa.cs.uno.edu/. Based on hundreds of test cases, we compare our algorithm with three other, commonly used methods: CE, Dali, and SSM. Our results show that, in most cases, our algorithm outputs a larger number of aligned positions when the (C(alpha)) RMSD is comparable. Also, in many cases where the number of aligned positions is larger or comparable to the other methods, our learning method is able to achieve a smaller (C(alpha)) RMSD than the other methods tested.