  The $g$-girth-thickness $\theta(g,G)$ of a graph $G$ is the smallest number
of planar subgraphs of girth at least $g$ whose union is $G$. In this paper, we
calculate the $4$-girth-thickness $\theta(4,G)$ of the complete $m$-partite
graph $G$ when each part has an even number of vertices.
