The available simple mapping functions are surveyed, and a new mapping function that provides for positive interference within chromosome arms and no interference across the centromere is proposed, together with the corresponding formula for centromeric linkage. This new function is derived by assuming that all chromosome arms except the short arms of acrocentric chromosomes hav an obligatory chiasma, and that the remaining chiasmata are distributed at random; assumptions which may correspond reasonably well to reality. A method for the comparison of the goodness of fit of mapping functions with family data is given. Low levels of interference seem to be indicated, although as yet insufficient human data is available to allow interference to the specified. Interference has a considerable effect on the estimation of map distances between loci from 3-point lod scores as is shown by the linkage group Rh, UMPK, PGM1, Amy, 1qh, Fy, on chromosome 1.