In the last three decades several hundred nearby members of young stellar moving groups (MGs) have been identified, but there has been less systematic effort to quantify or characterize young stars that do not belong to previously identified MGs. Using a kinematically unbiased sample of 225 lithium-rich stars within 100 pc, we find that only 50+/-10 per cent of young (<=125Myr), low-mass (0.5<M/M_{sun}_<1.0) stars, are kinematically associated with known MGs. Whilst we find some evidence that five of the non-MG stars may be connected with the Lower Centaurus-Crux association, the rest form a kinematically 'hotter' population, much more broadly dispersed in velocity, and with no obvious concentrations in space. The mass distributions of the MG members and non-MG stars are similar, but the non-MG stars may be older on average. We briefly discuss several explanations for the origin of the non-MG population.