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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 atthe origin, there do exist travelling wave solutions (actually those which are"rapid") of the nonlocal Fisher equation that connect the two homogeneoussteady states 0 (dynamically unstable) and 1. In particular this allowssituations where 1 is unstable in the sense of Turing. Our proof does notinvolve any maximum principle argument and applies to kernels with {\it fattails}.

Rapid travelling waves in the nonlocal Fisher equation connect two unstable states