A new thermodynamic Green's-function method is developed to handle interacting many-body systems containing a small subsystem with a fixed number of particles. The new method involves the use of the canonical ensemble and is more complicated than the usual Green's-function method. But, by means of the functional derivative technique, it is shown that systematic perturbative procedures are available and can be carried out in an entirely straight-forward manner. The example given in the present paper is the system of phonons interacting with a fixed number of fermions. It serves to illustrate the general formulation as well as perturbation calculation in the new method. © 1971 The American Physical Society.