  We consider Bernoulli (bond) percolation with parameter $p$ on the Cayley
tree of order $k$. We introduce the notion of zebra-percolation that is
percolation by paths of alternating open and closed edges. In contrast with
standard percolation with critical threshold at $p_c= 1/k$, we show that
zebra-percolation occurs between two critical values $p_{{\rm c},1}$ and
$p_{{\rm c},2}$ (explicitly given). We provide the specific formula of
zebra-percolation function.
