Let (Mr,T) be a smooth closed manifold of dimension r with a smooth involution T whose fixed point set is F=HP₁(2m)∪HP₂(2m)∪HP(2n+1)(m≥1)， where HP(n) denotes the n-dimensional quaternionic projective space. By constructing symmetric polynomial and computing characteristic number, it is proved that when r>8m+8n+8, every involution (Mr,T) fixes F bounds.