Given the DNA fingerprints of two individuals with some bands being shared by both individuals, we define a new measure of the degree of similarity between the DNA profiles of two individuals. We use this measure to calculate the expected DNA similarity of two unrelated individuals of a randomly mating population; this similarity is due to chance only. Then, the expected similarity between two related individuals is obtained; this similarity is due to chance andrelatedness. From these results, the degree of similarity due to relatedness alone may be calculated.