Cattaneo's relative formulation of relativistic mechanics is based on the covariant transverse derivative of an arbitrary totally spatial tensor field. On the other hand, Bressan bases relativistic elasticity, possibly with couple stresses, on the Lagrangian spatial derivative of an arbitrary double tensor. I give a chronotopic expression of the spatial projection of the Lagrangian derivative in the case that the reference configuration coincides with the one of the body on a locally time-orthogonal space-time section in $\mathcal{E}$. By the chronotopic expression above, I determine the relation between the two derivatives and prove the coincidence of the nine significative components. Furthermore I give a short proof of a fundamental theorem of Cattaneo on the transverse derivative.