  Let $G$ be a graph, and $Z$ a subset of its vertices, which we color black,
while the remaining are colored white. We define the skew color change rule as
follows: if $u$ is a vertex of $G$, and exactly one of its neighbors $v$, is
white, then change the color of $v$ to black. A set $Z$ is a skew zero forcing
set for $G$ if the application of the skew color change rule (as many times as
necessary) will result in all the vertices in $G$ colored black. A set $Z$ is a
minimum skew zero forcing set for $G$ if it is a skew zero forcing set for $G$
of least cardinality. The skew zero forcing number $\sZ (G)$ is the minimum of
$|Z|$ over all skew zero forcing sets $Z$ for $G$.
  In this paper we discuss graphs that have extreme skew zero forcing number.
We characterize complete multipartite graphs in terms of $\sZ (G)$. We note
relations between minimum skew zero forcing sets and matchings in some
bipartite graphs, and in unicyclic graphs. We establish that the elements in
the set of minimum skew zero forcing sets in certain bipartite graphs are the
bases of a matroid.
