  We derive analytic merger rates for dark-matter haloes within the framework
of the Extended Press-Schechter (EPS) formalism. These rates become
self-consistent within EPS once we realize that the typical merger in the limit
of a small time-step involves more than two progenitors, contrary to the
assumption of binary mergers adopted in earlier studies. We present a general
method for computing merger rates that span the range of solutions permitted by
the EPS conditional mass function, and focus on a specific solution that
attempts to match the merger rates in N-body simulations. The corrected EPS
merger rates are more accurate than the earlier estimates of Lacey & Cole, by
~20% for major mergers and by up to a factor of ~3 for minor mergers of mass
ratio 1:10^4. Based on the revised merger rates, we provide a new algorithm for
constructing Monte-Carlo EPS merger trees, that could be useful in
Semi-Analytic Modeling. We provide analytic expressions and plot numerical
results for several quantities that are very useful in studies of galaxy
formation. This includes (a) the rate of mergers of a given mass ratio per
given final halo, (b) the fraction of mass added by mergers to a halo, and (c)
the rate of mergers per given main progenitor. The creation and destruction
rates of haloes serve for a self-consistency check. Our method for computing
merger rates can be applied to conditional mass functions beyond EPS, such as
those obtained by the ellipsoidal collapse model or extracted from $N$-body
simulations.
