A theory of rearrangement collisions taking account of the nonorthogonality of initial and final states is presented. Detailed discussion of the range of validity of the theory is worked out. The method is applied to proton-hydrogen-atom charge exchange collisions. We find that at high energy the Jackson-Schiff results are obtained and that below 100 kev the cross section is raised significantly above the result of Jackson and Schiff. The new result is in better agreement with experimental results than the calculations based on the Jackson-Schiff formulation.