It is hypothesized that a splitting of the stratospheric polar vortex and a sudden warming can result when the polar vortex is elongated and a closed cyclonic circulation develops on a subplanetary scale in the troposphere beneath one of its tips. The hypothesis is supported by studying the splitting event in the Southern Hemisphere during spring 2002. Potential vorticity inversion and an inverse modelling technique using the adjoint of a fully nonlinear dynamical model are used to confirm that splitting is sensitive to subplanetary-scale cyclogenesis when it is strong. Examples of stratospheric vortex-splitting events in the Northern Hemisphere are consistent with the hypothesis. The proposed mechanism for splitting contrasts with the commonly accepted one that it is caused by the upward propagation of a planetary wave from the troposphere. It is suggested that the phenomenon is better understood as an example of a vortex interaction rather than as a wave–mean flow interaction.