The zone modulus is a conformally invariant functional over the space of two-component links embedded in R3 or S3. It is a positive real number and its lower bound is 1. Its main property is that the zone modulus of a non-split link is greater than (1 + p 2)2. In this paper, we will show that the only non-split links with modulus equal to (1+ p 2)2 are the Clifford links, that is, the conformal images of the standard geometric Hopf link.