Employing traditional Galerkin method, a coupled-mode flutter is predicted in the supercritical region of simply-supported pipes which constitutes a paradox since the internal flow effect is conservative and there is no energy to sustain the oscillation. Although there is a consensus that the flutter does not exist, the intrinsic mechanism remains to be clarified. This study has found that the internal flow induced Coriolis force term cannot be decoupled in traditional Galerkin method which leads to the dissatisfaction of the convergence conditions required in weighted residual approach (WRA). Moreover, the disparities in the predicted complex frequencies have been witnessed at different base function numbers when the internal flow velocity is sufficiently large. A modified Galerkin method adopting a new set of weighting functions is proposed based on WRA, and the Coriolis force term disappears by use of the orthogonality relations (it is stated that the Coriolis force is not directly omitted). Thus, a convergent solution for the set of residual functions which are identically equal to zeros can be guaranteed. Employing the modified method, the convergence in simulations is confirmed and the flutter phenomenon does not occur. This study can be a workbench for the study on the unsolved or partly solved issues in simulations of fluid-conveying pipes. Moreover, it has demonstrated that the predictions in traditional Galerkin method overestimate the natural frequencies, and it becomes more profound in higher-order natural modes at larger internal flow velocities which are of practice significance for dynamic analysis of flexible pipeline systems.