  We study the unitarized meson-baryon scattering amplitude at leading order in
the strangeness $S=-1$ sector using time-ordered perturbation theory for a
manifestly Lorentz-invariant formulation of chiral effective field theory. By
solving the coupled-channel integral equations with the full off-shell
dependence of the effective potential and applying subtractive renormalization,
we analyze the renormalized scattering amplitudes and obtain the two-pole
structure of the $\Lambda(1405)$ resonance. We also point out the necessity of
including higher-order terms.
