  The Hamilton-Waterloo problem with uniform cycle sizes asks for a $2-$
factorization of the complete graph $K_v$ (for odd {\em v}) or $K_v$ minus a
$1-$factor (for even {\em v}) where $r$ of the factors consist of $n-$cycles
and $s$ of the factors consist of $m-$cycles with $r+s=\left \lfloor
\frac{v-1}{2} \right \rfloor$. In this paper, the Hamilton-Waterloo Problem
with $4-$cycle and $m-$cycle factors for odd $m\geq 3$ is studied and all
possible solutions with a few possible exceptions are determined.
