  I present a new formalism of the R-matrix theory where the formal parameters
for the resonance energies and widths are identical to the observed values. By
allowing the boundary condition parameters to vary from level to level, the
freedom required to adjust the formal parameters for the pole positions to the
observed values is obtained. The basis of the resulting theory becomes
nonorthogonal, and I describe the procedure to construct a consistent R-matrix
theory with such a nonorthogonal basis. And by adjusting the normalization of
the states that form the basis, the formal parameters for the reduced decay
widths also become the same as those observed, leaving no formal parameters
that are different from the observed ones. A demonstration of the developed
theory to the elastic 12C+p scattering data is presented.
