Flow transition is a hot topic of fluid dynamics. The origin of turbulence has been discussed for several decades, but a convincing answer has yet to be found. Past research lacks a correct definition of a vortex, for instance, vorticity or the Q criterion have been used to detect vortexes. In 2018, Liutex was proposed as the correct mathematical definition of the vortex. The direction of Liutex aligns with the local vortex axis and the magnitude of Liutex is twice the angular speed. Given that the correct definition of a vortex has been proposed, there is a need to revisit the process of flow transition by using Liutex. In this paper, a DNS result of the flat plate boundary layer transition is used to analyze the initial stage of the flow transition. It was found that the spanwise vortex forms first, followed by the \(\Lambda \) vortex, and then the hairpin vortex. Linear stability theory is introduced to explain the mechanism of spanwise vortex formation. New findings of the vortex structures by applying Liutex core lines are provided in this paper.