By using a covariant isobar model and the latest experimental data we have analyzed the role of the P13(1900) and D13(2080) resonances in the kaon photoproduction process γp→K +Λ. Special attention has been paid to the region where the second peak in the cross section is located, i.e., at total c.m. energies around 1.9 GeV. It is found that this peak originates mostly from the P 13(1900) resonance contribution. Although the contribution of the D13(2080) resonance is not negligible, it is much smaller than that of the P13(1900) state. Our finding confirms that the P 13(1900) resonance is also important in explaining the beam-recoil double polarization data Cx and Cz, provided that the mass and the width of this resonance are 1871 and 131 MeV, respectively.