Genetic linkage analysis of human pedigrees using many linked markers simultaneously is a difficult computational problem. We have previously described an approach to this problem that uses hidden Markov models (HMMs) and is quite efficient for pedigrees of moderate size. Here, we describe a new, faster algorithm for the key step in the HMM calculation. The algorithm employs a fast Fourier transform on the group of pedigree inheritance patterns. It substantially improves the overall performance of the software package GENEHUNTER for performing linkage analysis. The Fourier representation opens up new research directions for pedigree analysis.