Large genealogies are potentially very informative for linkage analysis. However, the software available for exact non-parametric multipoint linkage analysis is limited with respect to the complexity of the families it can handle. A solution is to split the large pedigrees into sub-families meeting complexity constraints. Different methods have been proposed to "best" split large genealogies. Here, we propose a new procedure in which linkage is performed on several carefully chosen sub-pedigree sets from the genealogy instead of using just a single sub-pedigree set. Our multiple splitting procedure capitalizes on the sensitivity of linkage results to family structure and has been designed to control computational feasibility and global type I error. We describe and apply this procedure to the extreme case of the highly complex Hutterite pedigree and use it to perform a genome-wide linkage analysis on asthma. The detection of a genome-wide significant linkage for asthma on chromosome 12q21 illustrates the potential of this multiple splitting approach.