In a previous work, we explored the possibility that the β Pictoris moving group (BPMG), consisting of low-mass post-T Tauri stars, was formed near the Scorpius-Centaurus OB association. The cause of the formation could be a Type II supernova exploding either in Lower Centaurus Crux (LCC) or the Upper Centaurus Lupus (UCL), the two older subgroups of that association. Here we present new results for BPMG. A more detailed analysis of the orbit confinement in this group leads to a star distribution pattern at birth that can be considered as a representation of the density distribution in the natal cloud. We also propose a plausible origin for the supernova that could have triggered the star formation in BPMG by finding the past position of the runaway star HIP 46950. We find that this scenario is capable of explaining the origin of all the members of BPMG proposed by Zuckerman and coworkers and by Song and coworkers, with the exception of HIP 79881, which is probably an old main-sequence interloper.