Let (X1,X2,Xs) be a continuous, trivariate random vector for which it is of interest to compare the correlation betweenX1andX2with that betweenX3andX1. This problem is important, for example when bothX2andX3are potential linear predictors forX1or, more generally, whenever the variable (X1.X2,X3) represents a triplet of measurements on the same individual and correlation comparisons are desired. In this note it is shown that an exact distribution-free test for such problems can he based on a single Kendall correlation coellicient.