  In this paper the fine triangle intersection problem for a pair of maximum
kite packings is investigated. Let $Fin(v)={(s,t):$ $\exists$ a pair of maximum
kite packings of order $v$ intersecting in $s$ blocks and $s+t$ triangles$}$.
Let $Adm(v)={(s,t): s+t\leq b_v, s,t$ are non-negative integers$}$, where
$b_v=\lfloor v(v-1)/8\rfloor$. It is established that $Fin(v)= Adm(v)\setminus
{(b_v-1,0),(b_v-1,1)}$ for any integer $v\equiv 0,1 ({\rm mod} 8)$ and $v\geq
8$; $Fin(v)=Adm(v)$ for any integer $v\equiv 2,3,4,5,6,7 ({\rm mod} 8)$ and
$v\geq 4$.
