  The exquisitely measured maps of fluctuations in the Cosmic Microwave
Background (CMB) present the possibility to test the principle of Statistical
Isotropy (SI) of the Universe through systematic observable measures for
non-Statistical Isotropy (nSI) features in the data. Recent measurements of the
CMB temperature field provide tantalizing evidence of the deviation from SI. A
systematic approach based on strong mathematical formulation allows any nSI
feature to be traced to known physical effects or observational artefacts.
Unexplained nSI features could have immense cosmological ramifications for the
standard model of cosmology. BipoSH (Bipolar Spherical Harmonics) provides a
general formalism for quantifying the departure from statistical isotropy for a
field on a 2D sphere. We adopt a known reduction of the BipoSH functions,
dubbed Minimal Harmonics (Manakov et al. 1996). We demonstrate that this
reduction technique of BipoSH leads to a new generalized set of isotropic
angular correlation functions (mBipoSH) that are observable quantifications of
nSI features in a sky map. We show that any nSI feature in the CMB map captured
by BipoSH at the bipolar multiple $L$ with projection $M$ can be studied by
$(L+1)$ mBipoSH angular correlation functions in case of even parity and by $L$
functions in case of odd parity. We present in this letter a novel observable
quantification of deviation from statistical isotropy in terms of generalized
angular correlation functions that are compact and complementary to the BipoSH
spectra that generalize angular power spectrum CMB fluctuations.
