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In this note, adopting the pullback formalism of global Finsler geometry, weshow by a counterexample that the kernel $\text{Ker}_R$ of the h-curvature $R$of Cartan connection and the associated nullity distribution $\N_R$ do notcoincide, contrary to Akbar-Zadeh's result \cite{akbar.nul3.}. We givesufficient conditions for $\text{Ker}_R$ and $\N_R$ to coincide.

A note on "Sur le noyau de l'op\'{e}rateur de courbure d'une vari\'{e}t\'{e} finsl\'{e}rienne" [C. R. Acad. Sci. Paris, t. 272 (1971), 807-810]