We have investigated the effects of spin-7/2 and-9/2 nucleon resonances in the kaon photoproduction process γp→K+Λ. To this end, the corresponding propagators were derived from the generalized spin projection operators. To remove the lower spin backgrounds in the scattering amplitude, we used the vertex factors obtained from the consistent interaction Lagrangians inspired by Pascalutsa and Vrancx et al. The scattering amplitude was included in our previous isobar model, and the effects of four nucleon resonances with spins 7/2 and 9/2 listed by the Particle Data Group were investigated by making use of all available kaon photoproduction data. A significant improvement to our previous model has been observed in all observables, especially in the beam-recoil double-polarization observables Cx, Cz, Ox′, and Oz′.