The original nonparametric (or model-free) method of linkage analysis that was described by Haseman and Elston in 1972 (1) was designed for analysis of quantitative traits using the sib-pair study design. In the following subheading, a brief introduction to linear regression precedes a description of the traditional and new Haseman-Elston theory. The Methods, Interpretation, and Worked Example sections of the chapter are all based on the programs GENIBD and SIBPAL2 from the S.A.G.E. Version 4.0 Beta 5 software package. SIBPAL2 is currently the only software publicly available for carrying out the new Haseman-Elston method.