Nonlinear response of a four-level atomic system with two closely lying intermediate levels to the incoherent pump field is investigated. It is shown that without coherent laser control field and just by quantum interference of incoherent pumping field and spontaneous emission, a giant Kerr nonlinearity can be achieved. It is also demonstrated that the enhanced Kerr nonlinearity is located in the reduced absorption region. In addition, the effect of direct and indirect incoherent pump rates on Kerr nonlinearity is then discussed.
