  The antenna subtraction method has been successfully applied to a wide range
of processes relevant for the Large Hadron Collider at next-to-next-to-leading
order in $\alpha_s$ (NNLO). We propose an algorithm for building antenna
functions for any number of real emissions from an identified pair of hard
radiator partons directly from a specified list of unresolved limits. We use
the algorithm to explicitly build all single- and double-real QCD antenna
functions and compare them to the previous antenna functions, which were
extracted from matrix elements. The improved antenna functions should be more
easily applicable to NNLO subtraction terms. Finally, we match the integration
of the antenna functions over the final-final unresolved phase space to the
previous incarnation, serving as an independent check on our results.
