We present a new algorithm which groups the subhaloes found in cosmological N-body simulations by structure finders such as SUBFIND into dark matter haloes whose formation histories are strictly hierarchical. One advantage of these 'Dhaloes' over the commonly used friends-of-friends (FoF) haloes is that they retain their individual identity in the cases when FoF haloes are artificially merged by tenuous bridges of particles or by an overlap of their outer diffuse haloes. Dhaloes are thus well suited for modelling galaxy formation and their merger trees form the basis of the Durham semi-analytic galaxy formation model, GALFORM. Applying the Dhalo construction to the ... cold dark matter Millennium II Simulation, we find that approximately 90 per cent of Dhaloes have a one-to-one, bijective match with a corresponding FoF halo. The remaining 10 per cent are typically secondary components of large FoF haloes. Although the mass functions of both types of haloes are similar, the mass of Dhaloes correlates much more tightly with the virial mass, ..., than FoF haloes. Approximately 80 per cent of FoF and bijective and non-bijective Dhaloes are relaxed according to standard criteria. For these relaxed haloes, all three types have similar concentration-M200 relations and, at fixed mass, the concentration distributions are described accurately by log-normal distributions. (ProQuest: ... denotes formulae/symbols omitted.)