Tandem repeat sequences have been found in great numbers in proteins that are conserved in a wide range of living species. In order to reconstruct the evolutionary history of such sequences, it is necessary to develop algorithms and methods that can work with highly divergent motifs. Here we propose a reconstruction algorithm that uses, in parallel, ortholog tandem repeat sequences from n species whose phylogeny is known, allowing it to distinguish mutations that occurred before and after the first speciation. At each step of the reconstruction, both the boundaries and the length of the duplicated segment are recalculated, making the approach suitable for sequences for which the fixed boundary hypothesis may not hold. We use this algorithm to reconstruct a 4-bladed ancestor of the 7-bladed WD40 beta-propeller, using orthologs of the GNB1 human protein in plants, yeasts, nematodes, insects and fishes. The results obtained for the WD40 repeats are very encouraging, as the noise in the duplication reconstruction is significantly reduced.