According to the resonance scattering theory, a process of background subtraction is always required to obtain the resonance spectrum of a target. A new formulation of the theory is proposed here in which the background subtraction is not necessary and the resonance spectrum can be obtained directly. Contrary to the previous theory, this formulation suggests that, within each partial wave, there are three contributions: the resonance, the background, and their correlation. Also, it is shown that the resonance contribution (at least for empty elastic shells) can be synthesized by considering the resonances of Breit–Wigner form and their pair correlation.