Inferences derived from large multiple alignments of biological sequences are critical to many areas of biology, including evolution, genomics, biochemistry, and structural biology. However, the complexity of the alignment problem imposes the use of approximate solutions. The most common is the progressive algorithm, which starts by aligning the most similar sequences, incorporating the remaining ones following the order imposed by a guide-tree. We developed and validated on protein sequences a regressive algorithm that works the other way around, aligning first the most dissimilar sequences. Our algorithm produces more accurate alignments than non-regressive methods, especially on datasets larger than 10,000 sequences. By design, it can run any existing alignment method in linear time thus allowing the scale-up required for extremely large genomic analyses.