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In this work we study the decomposability property of branched coverings ofdegree $d$ odd, over the projective plane, where the covering surface has Eulercharacteristic $\leq 0$. The latter condition is equivalent to say that thedefect 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 isrealizable by an indecomposable branched covering over the projective plane.The case when $d$ is even is known.

Indecomposable branched coverings over the projective plane by surfaces $M$ with $\chi(M) \leq 0$