  By introducing the notion of relative derangements of type $B$, also called
signed relative derangements, which are defined in terms of signed
permutations, we obtain a type $B$ analogue of the well-known relation between
relative derangements and the classical derangements. While this fact can be
proved by using the principle of inclusion and exclusion, we present a
combinatorial interpretation with the aid of the intermediate structure of
signed skew derangements.
