  In this note we study half-BPS operators in N=4 super Yang-Mills for gauge
group SU(N) at finite N. In particular we elaborate on the results of
hep-th/0410236, providing an exact formula for the null basis operators
algorithmically constructed there. For gauge groups U(N) and SU(N) we show that
this basis is dual to the basis of multi-trace operators with respect to the
two point function. We use this to extend the results of hep-th/0611290
concerning factorisation and probabilities from U(N) to SU(N). We also give a
construction for a separate diagonal basis of the SU(N) operators in terms of
the higher Hamiltonians of the complex matrix model reduction of this sector.
