The weighted pairwise correlation (WPC) approach provides simple and flexible tests for genetic linkage which may be adapted to qualitative, quantitative or age-dependent traits. These tests also seem to have good power. However, when working with large pedigrees, a disease susceptibility gene not linked to the marker studied induces correlations of the trait values, leading to inflated type I errors for these tests. We propose here a new approach for inference based on the randomization of the alleles following the Mendelian laws and conditioning on the alleles of the founders. This approach is applied to the analysis of the quantitative traits in a set of simulated pedigrees. The alpha posteriori comparison of the findings to the true model indicates directions for future work.