The internal flow effect of a simply-supported pipe is conservative， since the system does not gain or lose energy in the course of vibration. Based on linear analysis via traditional Galerkin method， when the internal flow velocity exceeds a critical val?ue， a coupled-mode flutter occurs， which constitutes a paradox as there is no energy to sustain the oscillation. Although it has dem?onstrated that the flutter does not exist adopting nonlinear analysis method， the paradox remains to be clarified. From linear analysis viewpoint， internal flow introduces centrifugal force， Coriolis force and initial force. Coriolis matrix is skew-symmetric （antisymmetric）. A modified Galerkin method is proposed based on the weighted residual approach. The Coriolis force term disappears by using the orthogonality of the weighting functions and base functions and the dynamic equation can be fully decoupled. The natural frequencies of a flexible pipe system are predicted via the modified method. The predictions in the subcritical region fit well with literature and the flutter phenomenon does not appear. An explanation is given for the paradox. Moreover， it has demonstrated that the predictions by traditional Galerkin method overestimate the natural frequencies， and it becomes more obvious in higher-order modes at larger internal flow velocities.