  In this paper we demonstrate an efficient method for including both CMB
temperature and polarisation data in optimal non-Gaussian estimators. The
method relies on orthogonalising the multipoles of the temperature and
polarisation maps and results in a reduction by a factor of over 3 the terms
required to calculate the estimator. The method is illustrated with the modal
method applied to bispectrum estimation via the CMB with the trispectrum
included as an appendix. However, the method is quite general and can be
applied to any optimal bispectrum or trispectrum estimator including the KSW,
binned and wavelet approaches. It would also be applicable to any situation
where multiple data sets with known correlations are being considered.
