  Suppose $k \ge 2$ is an integer. Let $Y_k$ be the poset with elements $x_1,
x_2, y_1, y_2, \ldots, y_{k-1}$ such that $y_1 < y_2 < \cdots < y_{k-1} < x_1,
x_2$ and let $Y_k'$ be the same poset but all relations reversed. We say that a
family of subsets of $[n]$ contains a copy of $Y_k$ on consecutive levels if it
contains $k+1$ subsets $F_1, F_2, G_1, G_2, \ldots, G_{k-1}$ such that
$G_1\subset G_2 \subset \cdots \subset G_{k-1} \subset F_1, F_2$ and $|F_1| =
|F_2| = |G_{k-1}|+1 =|G_{k-2}|+ 2= \cdots = |G_{1}|+k-1$. If both $Y_k$ and
$Y'_k$ on consecutive levels are forbidden, the size of the largest such family
is denoted by $\mathrm{La}_{\mathrm{c}}(n, Y_k, Y'_k)$. In this paper, we will
determine the exact value of $\mathrm{La}_{\mathrm{c}}(n, Y_k, Y'_k)$.
