Multipoint linkage methods are powerful tools that are often employed as the first means to discover alleles affecting liability to diseases. With the advent of dense marker maps, linkage disequilibrium (LD) between markers is inevitable and it comes at the cost of bias and an increased rate of false-positive findings for linkage analyses that assume alleles of different markers are independent. I propose a “multipoint on subsets” method that avoids this issue by partitioning the markers into interlaced and non-overlapping subsets. Each subset is analyzed separately, their statistics are then averaged, and the resulting average is standardized by its estimated standard deviation. In addition to being robust to the challenges induced by dependent marker alleles, data simulated under linkage equilibrium show that the proposed method does not suffer any detectable loss of power when compared to traditional methods. Genet. Epidemiol. 2005. © 2005 Wiley-Liss, Inc.