  We prove that for Bernoulli percolation on a graph
$\mathbb{Z}^2\times\{0,\dots,k\}$ ($k\ge 0$), there is no infinite cluster at
criticality, almost surely. The proof extends to finite range Bernoulli
percolation models on $\mathbb{Z}^2$ which are invariant under $\pi/2$-rotation
and reflection.
