We study kaon-nucleon systems in the Skyrme model in a method based on the bound state approach of Callan-Klebanov but with the kaon around the physical nucleon of the rotating hedgehog. This corresponds to the variation after projection, reversing the order of semiclassical quantization of 1 /Nc expansion. The method, however, is considered to be suited to the study of weakly interacting kaon-nucleon systems including loosely K ¯N bound states such as Λ (1405 ). We have found a bound state with binding energy of order 10 MeV, consistent with the observed state. We also discuss the K ¯N interaction and find that it consists of an attraction in the middle range and a repulsion in the short range.