A new systematical method which enables us to describe an electron gas in terms of bosons is developed. This boson corresponds to an “exciton”, i.e. a pair of an electron outside the Fermi sphere and a hole inside. The formalism is particularly suitable to the system at high density, as suggested by Sawada's discussion of the same system. As a straightforward application, the effect of electron exchange on the plasma frequency is calculated. The result coincides with that of a Hartree-Fock treatment.