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Following the equation of motion method and Green's function technique, the coexistence of itinerant ferromagnetism (FM) and superconductivity (SC) is investigated in a single band homogeneous system. Self-consistent equations for superconducting order parameter (Δ) and magnetic order parameter (ΔFM) are derived. It is shown that there generally exists a coexistent (Δ ≠ 0 and ΔFM ≠ 0) solutions to the coupled equations of the order parameter in the temperature range 0<TTC, TFM) where TC and TFM are respectively the superconducting and ferromagnetic transition temperatures. Expressions for the specific heat, density of states and free energy are derived. The specific heat has a linear temperature dependence at low temperatures as opposed to the exponential decrease in the BCS theory. The density of states for a finite ΔFM increases as opposed to that of a standard ferromagnetic metal. The free energy shows that the superconducting ferromagnetic state has lower energy than the normal ferromagnetic state and therefore is realized at low enough temperature. The theory is applied to explain the observations of URhGe. The agreement between theory and experimental results is quite satisfactory.