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It is widely hoped that constructing a complete human haplotype map will help to associate complex diseases with certain SNP's. Unfortunately, the number of SNP's is huge and it is very costly to sequence many individuals. Therefore, it is desirable to reduce the number of SNP's that should be sequenced to considerably small number of informative representatives, so called tag SNP's. In this paper, we propose a new linear algebra based method for selecting and using tag SNP's. Our method is purely combinatorial and can be combined with linkage disequilibrium (LD) and block based methods. We measure the quality of our tag SNP selection algorithm by comparing actual SNP's with SNP's linearly predicted from linearly chosen tag SNP's. We obtain an extremely good compression and prediction rates. For example, for long haplotypes (>25000 SNP's), knowing only 0.4% of all SNP's we predict the entire unknown haplotype with 2% accuracy while the prediction method is based on a 10% sample of the population.