The Milne problem is studied for the case of, one-speed, time independent, plane symmetric Boltzmann equation, for which the scattering law is isotropic scattering with a backward leak. First of all, the new solution for the angular flux is expressed in terms of the solution of the Boltzmann equation with isotropic scattering. The expansion coefficients are determined by the resulting new boundary condition and orthogonality relations. The results for the expansion coefficients are given in the form of exact integral equations, but the numerical values for the extrapolated endpoint are obtained for the first order approximate coefficients. The variation of the extrapolated endpoint with β, the degree of backward anisotropy agrees in general with the previous findings.