  We introduce a process, that we call "shearing", which for any given normal
Loewner chain produces a normal Loewner chain made of shears automorphisms. As
an application, and in stringent contrast to the one-dimensional case, we prove
the existence of a starlike bounded function in the class $S^0$ of the ball
$\mathbb B^2$ (in fact the restriction of a shear automorphism of $\mathbb
C^2$) which is a support point for a linear continuous functional.
