  In this note, we give a positive answer to a question addressed in
\cite{Nad-Per-Tan}. Precisely we prove that, for any kernel and any slope at
the origin, there do exist travelling wave solutions (actually those which are
"rapid") of the nonlocal Fisher equation that connect the two homogeneous
steady states 0 (dynamically unstable) and 1. In particular this allows
situations where 1 is unstable in the sense of Turing. Our proof does not
involve any maximum principle argument and applies to kernels with {\it fat
tails}.
