  In this paper we study the class of "shearing" holomorphic maps of the unit
ball of the form $(z,w)\mapsto (z+g(w), w)$. Besides general properties, we use
such maps to construct an example of a normalized univalent map of the ball
onto a Runge domain in $\mathbb C^n$ which however cannot be embedded into a
Loewner chain whose range is $\mathbb C^n$.
