The rigorous nonorthogonal vectorial coupled-mode theory is presented for the isotropic waveguide with isotropic disturbances,based on the Maxwell Equation. The coupling term due to polarization,which is presented in the scalar coupled-mode theory with the vector correction of the Wei-Ping Huang,isn't included in this rigorous vectorial coupled-mode theory,and the term is emerged during the derivation. It is because that the coupling term due to polarization and the ignored term due to the weakly guiding approximation are as small as the second order,and they are just the same. Therefore,the rigorous vectorial coupled-mode theory has not the coupling term due to polarization which can be looked as the vector correction for the scalar coupled-mode theory.