  We report on a theoretical study of the $K^- p \to \eta \Lambda$ reaction
near threshold by using an effective Lagrangian approach. The role of
$s-$channel $\Lambda(1670)$, $t-$channel $K^*$ and $u-$channel proton pole
diagrams are considered. We show that the total cross sections data are well
reproduced. However, only including the $s-$wave $\Lambda(1670)$ state and the
background contribution from $t-$ and $u-$channel are not enough to describe
the bowl structures in the angular distribution of $K^- p \to \eta \Lambda$
reaction, which indicates that there should be higher partial waves
contributing to this reaction in some energy region. Indeed, if we considered
the contributions from a $D_{03}$ resonance, we can describe the bowl
structures, however, a rather small width ($\sim 2$ MeV) of this resonance is
needed.
