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Efficient haplotype matching search is of great interest when large genotyped cohorts are becoming available. Positional Burrows-Wheeler Transform (PBWT) enables efficient searching for blocks of haplotype matches. However, existing efficient PBWT algorithms sweep across the haplotype panel from left to right, capturing all exact matches. As a result, PBWT does not account for mismatches. It is also not easy to investigate the patterns of changes between the matching blocks. Here, we present an extension to PBWT, called bi-directional PBWT that allows the information about the blocks of matches to be present at both sides of each site. We also present a set of algorithms to efficiently merge the matching blocks or examine the patterns of changes on both sides of each site. The time complexity of the algorithms to find and merge matching blocks using bi-directional PBWT is linear to the input size. Using real data from the UK Biobank, we demonstrate the run time and memory efficiency of our algorithms. More importantly, our algorithms can identify more blocks by enabling tolerance of mismatches. Moreover, by using mutual information (MI) between the forward and the reverse PBWT matching block sets as a measure of haplotype consistency, we found the MI derived from European samples in the 1000 Genomes Project is highly correlated (Spearman correlation r=0.87) with the deCODE recombination map.