  In this paper, we show that the H\'enon map $\varphi_{a,b}$ has a generically
unfolding cubic tangency for some $(a,b)$ arbitrarily close to $(-2,0)$ by
applying results of Gonchenko-Shilnikov-Turaev [12]-[16]. Combining this fact
with theorems in Kiriki-Soma [20], one can observe the new phenomena in the
H\'enon family, appearance of persistent antimonotonic tangencies and cubic
polynomial-like strange attractors.
