A kite-design of order n is a decomposition of the complete graph Kn into kites. Such systems exist precisely when n ≡ 0,1 (mod 8). Two kite systems (X,K1) and (X,K2) are said to intersect in m pairwise disjoint blocks if |K1∩K2| = m and all blocks in K1∩K2 are pairwise disjoint. In this paper we determine all the possible values of m such that there are two kite-designs of order n intersecting in m pairwise disjoint blocks, for all n ≡ 0,1 (mod 8).
