  The antenna-subtraction technique has demonstrated remarkable effectiveness
in providing next-to-next-to-leading order in $\alpha_s$ (NNLO) predictions for
a wide range of processes relevant for the Large Hadron Collider. In a previous
paper [1], we demonstrated how to build real-radiation antenna functions for
any number of real emissions directly from a specified list of unresolved
limits. Here, we extend this procedure to the mixed case of real and virtual
radiation, for any number of real and virtual emissions. A novel feature of the
algorithm is the requirement to match the antenna constructed with the correct
unresolved limits to the other elements of the subtraction scheme. We discuss
how this can be achieved and provide a full set of real-virtual NNLO antenna
functions (together with their integration over the final-final unresolved
phase space). We demonstrate that these antennae can be combined with the
real-radiation antennae of Ref. [1] to form a consistent NNLO subtraction
scheme that cancels all explicit and implicit singularities at NNLO. We
anticipate that the improved antenna functions should be more amenable to
automation, thereby making the construction of subtraction terms for more
complicated processes simpler at NNLO.
