  Bredon and Wood have given a complete answer to the embeddability question
for nonorientable surfaces in lens spaces. They formulate their result in terms
of a recursive formula that determines, for a given lens space, the minimal
genus of embeddable nonorientable surfaces. Here we give a direct proof that,
amongst lens spaces as target manifolds, the Klein bottle embeds into
$L(4n,2n\pm 1)$ only. We describe four explicit realisations of these
embeddings.
