  Following Alspach and Parsons, a {\em metacirculant graph} is a graph
admitting a transitive group generated by two automorphisms $\rho$ and
$\sigma$, where $\rho$ is $(m,n)$-semiregular for some integers $m \geq 1$, $n
\geq 2$, and where $\sigma$ normalizes $\rho$, cyclically permuting the orbits
of $\rho$ in such a way that $\sigma^m$ has at least one fixed vertex. A {\em
half-arc-transitive graph} is a vertex- and edge- but not arc-transitive graph.
In this article quartic half-arc-transitive metacirculants are explored and
their connection to the so called tightly attached quartic half-arc-transitive
graphs is explored. It is shown that there are three essentially different
possibilities for a quartic half-arc-transitive metacirculant which is not
tightly attached to exist. These graphs are extensively studied and some
infinite families of such graphs are constructed.
