The symbol K(B,C) denotes a directed graph with the vertex set B∪C for two (not necessarily disjoint) vertex sets B,C in which an arc goes from each vertex of B into each vertex of C. A subdigraph of a digraph D which has this form is called a bisimplex in D. A biclique in D is a bisimplex in D which is not a proper subgraph of any other and in which B ≠ ∅ and C ≠ ∅. The biclique digraph C→ (D) of D is the digraph whose vertex set is the set of all bicliques in D and in which there is an arc from K(B1, C1) into K(B2, C2) if and only if C1 ∩ B2 = ∅. The operator which assigns C→ (D) to D is the biclique operator C→ . The paper solves a problem of E. Prisner concerning the periodicity of C→ .