In this paper, the fine triangle intersection problem for a pair of maximum kite packings is investigated. Let Fin（v） = {（s, t） ： E← a pair of maximum kite packings of order v intersecting in s blocks and s ＋ t triangles}. Let Adm（v） = {（s,t） ： s ＋ t≤by, s, t are non-negative integers}, where by = [v（v - 1）/8]. It is established that Fin（v） = Adm（v）／{（bv - 1,0）, （by - 1, 1）} for any integer v - 0, 1 （rood 8） and v ≥ 8; Fin（v） = Adm（v） for any integer v = 2, 3, 4, 5, 6, 7 （rood 8） and v≥ 4.
