  The burnt pancake graph $BP_n$ is the Cayley graph of the hyperoctahedral
group using prefix reversals as generators. Let $\{u,v\}$ and $\{x,y\}$ be any
two pairs of distinct vertices of $BP_n$ for $n\geq 4$. We show that there are
$u-v$ and $x-y$ paths whose vertices partition the vertex set of $BP_n$ even if
$BP_n$ has up to $n-4$ faulty elements. On the other hand, for every $n\ge3$
there is a set of $n-2$ faulty edges or faulty vertices for which such a
fault-free disjoint path cover does not exist.
