The likelihood approach is common in linkage analysis of large extended pedigrees. Various peeling procedures, based on the conditional independence of separate parts of a pedigree, are typically used for likelihood calculations. A peeling order may significantly affect the complexity of such calculations, particularly for pedigrees with loops or when many pedigrees members have unknown genotypes. Several algorithms have been proposed to address this problem for pedigrees with loops. However, the problem has not been solved for pedigrees without loops until now. In this paper, we suggest a new graph theoretic algorithm for optimal selection of peeling order in zero-loop pedigrees with incomplete genotypic information. It is especially useful when multiple likelihood calculation is needed, for example, when genetic parameters are estimated or linkage with multiple marker loci is tested. The algorithm can be easily introduced into the existing software packages for linkage analysis based on the Elston-Stewart algorithm for likelihood calculation. The algorithm was implemented in a software package PedPeel, which is freely available at http://mga.bionet.nsc.ru/nlru/.