  We consider a branching random walk on the line. Biggins and Kyprianou [6]
proved that, in the boundary case, the associated derivative martingale
converges almost surly to a finite nonnegative limit, whose law serves as a
fixed point of a smoothing transformation (Mandelbrot's cascade). In the
present paper, we give a necessary and sufficient condition for the
non-triviality of this limit and establish a Kesten-Stigum-like result.
