On the Riemann sphere, we consider the Ptolemaic characteristic of a four of non-empty pairwise non-intersecting compact subsets (generalized tetrad, or generalized angle). We obtain an estimate for distortion of this characteristic under the inverse to a K-quasimeromorphic mapping of the Riemann sphere which takes each of its values at no more than N different points. The distortion function in this estimate depends only on K and N. In the case K = 1, it is an essentially new property of complex rational functions.