Bessa [Be] proved that for given $n$ and ${{i}_{0}}$, there exists an $\varepsilon (\text{n,}\,{{i}_{0}})\,>\,0$ depending on $n$, ${{i}_{0}}$ such that if $M$ admits a metric $g$ satisfying $\text{Ri}{{\text{c}}_{(M,g)}}\ge n-1,\text{in}{{\text{j}}_{(M,g)}}\ge {{i}_{0}}\,>\,0$ and $\text{dia}{{\text{m}}_{(M,g)}}\,\ge \,\pi \,-\,\varepsilon $, then $M$ is diffeomorphic to the standard sphere. In this note, we improve this result by replacing a lower bound on the injectivity radius with a lower bound of the conjugate radius.