Abstract Background We have developed a new computational algorithm, Shape-IT, to infer haplotypes under the genetic model of coalescence with recombination developed by Stephens et al in Phase v2.1. It runs much faster than Phase v2.1 while exhibiting the same accuracy. The major algorithmic improvements rely on the use of binary trees to represent the sets of candidate haplotypes for each individual. These binary tree representations: (1) speed up the computations of posterior probabilities of the haplotypes by avoiding the redundant operations made in Phase v2.1, and (2) overcome the exponential aspect of the haplotypes inference problem by the smart exploration of the most plausible pathways (ie. haplotypes) in the binary trees. Results Our results show that Shape-IT is several orders of magnitude faster than Phase v2.1 while being as accurate. For instance, Shape-IT runs 50 times faster than Phase v2.1 to compute the haplotypes of 200 subjects on 6,000 segments of 50 SNPs extracted from a standard Illumina 300 K chip (13 days instead of 630 days). We also compared Shape-IT with other widely used software, Gerbil, PL-EM, Fastphase, 2SNP, and Ishape in various tests: Shape-IT and Phase v2.1 were the most accurate in all cases, followed by Ishape and Fastphase. As a matter of speed, Shape-IT was faster than Ishape and Fastphase for datasets smaller than 100 SNPs, but Fastphase became faster -but still less accurate- to infer haplotypes on larger SNP datasets. Conclusion Shape-IT deserves to be extensively used for regular haplotype inference but also in the context of the new high-throughput genotyping chips since it permits to fit the genetic model of Phase v2.1 on large datasets. This new algorithm based on tree representations could be used in other HMM-based haplotype inference software and may apply more largely to other fields using HMM.