  In this work we study the decomposability property of branched coverings of
degree $d$ odd, over the projective plane, where the covering surface has Euler
characteristic $\leq 0$. The latter condition is equivalent to say that the
defect of the covering is greater than $d$. We show that, given a datum
$\mathscr{D}=\{D_{1},\dots,D_{s}\}$ with an even defect greater than $d$, it is
realizable by an indecomposable branched covering over the projective plane.
The case when $d$ is even is known.
