The Kondo effect in a superconductor is investigated by using the double time Green function method of Nagaoka. It is shown that the exact solution of the Bloomfield-Hamann type can be obtained in this case. The main difference is the presence of the energy gap in the state density function, and the solution is shown to have some arbitrary functions arising from this energy gap. Using this solution and taking the simplest form for the arbitrary function, the position of the bound state in the energy gap is investigated. It is shown that the bound state exists for antiferromagnetic coupling, but not for ferromagnetic one. It is also shown that our result does not coincide with those of Fowler and Maki or of Soda et al., but coincides with the exact result in the classical limit.