  We present a new Monte-Carlo algorithm to generate merger trees describing
the formation history of dark matter halos. The algorithm is a modification of
the algorithm of Cole et al (2000) used in the GALFORM semi-analytic galaxy
formation model. As such, it is based on the Extended Press-Schechter theory
and so should be applicable to hierarchical models with a wide range of power
spectra and cosmological models. It is tuned to be in accurate agreement with
the conditional mass functions found in the analysis of merger trees extracted
from the LCDM Millennium N-body simulation. We present a comparison of its
predictions not only with these conditional mass functions, but also with
additional statistics of the Millennium Simulation halo merger histories. In
all cases we find it to be in good agreement with the Millennium Simulation and
thus it should prove to be a very useful tool for semi-analytic models of
galaxy formation and for modelling hierarchical structure formation in general.
We have made our merger tree generation code and code to navigate the trees
available at http://star-www.dur.ac.uk/~cole/merger_trees .
