  Let $M$ be a smooth closed $4k$-manifold whose Yamabe invariant $Y(M)$ is
nonpositive. We show that $$Y(M\sharp l \Bbb HP^k\sharp m \bar{\Bbb
HP^k})=Y(M),$$ where $l,m$ are nonnegative integers, and $\Bbb HP^k$ is the
quaternionic projective space. When $k=4$, we also have $$Y(M\sharp l
CaP^2\sharp m \bar{CaP^2})=Y(M),$$ where $CaP^2$ is the Cayley plane.
