  In this paper, we define the $4$-girth-thickness $\theta(4,G)$ of a graph $G$
as the minimum number of planar subgraphs of girth at least $4$ whose union is
$G$. We obtain the $4$-girth-thickness of the arbitrary complete graph $K_n$
getting that $\theta(4,K_n)=\left\lceil \frac{n+2}{4}\right\rceil$ for
$n\not=6,10$ and $\theta(4,K_6)=3$.
