The robust or model-free method for detecting linkage developed by Haseman and Elston for data from sib pairs is extended to incorporate observations of multiple traits on each individual. A method is proposed that estimates the linear function that results in the strongest correlation between the squared pair differences in the trait measurements and identity by descent at a marker locus. The method is illustrated by the study of apolipoprotein and cholesterol levels in individuals from a large family that had many members diagnosed with coronary heart disease.