  James' effective Hamiltonian method has been extensively adopted to
investigate largely detuned interacting quantum systems. This method is just
corresponding to the second-order perturbation theory, and cannot be exploited
to treat the problems which should be solved by using the third or higher-order
perturbation theory. In this paper, we generalize James' effective Hamiltonian
method to the higher-order case. Using the method developed here, we reexamine
two examples published recently [Phys. Rev.Lett. 117, 043601 (2016), Phys. Rev
A 92, 023842 (2015)], our results turn out to be the same as the original ones
derived from the third-order perturbation theory and adiabatic elimination
method respectively. For some specific problems, this method can simplify the
calculating procedure, and the resultant effective Hamiltonian is more general.
