  It is well known that the derangement numbers $d_n$, which count permutations
of length $n$ with no fixed points, satisfy the recurrence
$d_n=nd_{n-1}+(-1)^n$ for $n\ge1$. Combinatorial proofs of this formula have
been given by Remmel, Wilf, D\'esarm\'enien and Benjamin--Ornstein. Here we
present yet another, arguably simpler, bijective proof.
