One of Henderson’s important contributions was on the discovery of simple rules to compute the inverse of the numerator relationship matrix without the need for construction of the numerator relationship matrix. Recent development in genomic technology made it possible for animals to be genotyped for large numbers of SNPs. Two approaches have been proposed for inclusion of SNP data into national genetic evaluation systems for livestock: single-step and multiple-step procedures. The single-step procedure requires the inversion of the **G**-matrix which is currently computationally intensive and therefore not suitable for large-scale genetic evaluation. One of the main bottlenecks in the computation of the **G**^{-1} using the procedure proposed by Faux is the construction of the **T**^{-1}. We propose a recursive method for the computation of some elements of the **T**^{1}. The proposed method could circumvent computational challenges associated with Faux’s method.

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%B Proceedings of the World Congress on Genetics Applied to Livestock Production
%V Genetic Improvement Programs: Selection using molecular information (Posters)
%P 503
%G eng
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