Let V = {α1, α2,…, αn} be a finite set with n ≥ 2 and Pn(V) the set of all primitive binary relations on V. For Q ∈ Pn(V), denote by G(Q) the directed graph corresponding to Q.For positive integer d ≤ n, let Pn(V, d) = {Q:Q ∈ Pn(V) and G(Q) contains exactly d loops}. In this paper, it is proved that the set of common consequent indices of binary relations in Pn(V, d) is {1, 2 , n - [d/2]}. Furthermore, the minimal extremal binary relations are described.