In this paper the intersection problem for a pair of kite-GDDs of type 4u is investigated. The intersection problem for kite-GDDs is the determination of all pairs (T, s) such that there exists a pair of kite-GDDs (X,H ,B1) and (X,H ,B2) of the same type T and |B1∩B2| = s. Let J(u) = {s : ∃ a pair of kite-GDDs of type 4u intersecting in s blocks}; I(u) = {0, 1, . . . , bu − 2, bu}, where bu = 2u(u − 1) is the number of blocks of a kite-GDD of type 4u. We show that for any positive integer u ≥ 3, J(u) = I(u).