  In commutative algebra, if $\delta$ is a locally nilpotent derivation of the
polynomial algebra $K[x_1,\ldots,x_d]$ over a field $K$ of characteristic 0 and
$w$ is a nonzero element of the kernel of $\delta$, then $\Delta=w\delta$ is
also a locally nilpotent derivation with the same kernel as $\delta$. In this
paper we prove that the locally nilpotent derivation $\Delta$ of the free
associative algebra $K\langle X,Y\rangle$ is determined up to a multiplicative
constant by its kernel. We show also that the kernel of $\Delta$ is a free
associative algebra and give an explicit set of its free generators.
