A note on localization of pretriangulated categories

For a localising class $\mathcal S$ of morphisms in a pretriangulated category $\mathcal D$, a weak version of a sufficient condition that guarantees carrying the structure of pretriangulated category onto the localisation $\mathcal{D[S}^{-1}]$ is proposed. Moreover, we get a similar weakness of a sufficient condition in the context of triangulated categories.