In this work, we investigate the transition of a hexagonal patterned self-organised barrier discharge into a stochastic distributed pattern during voltage reduction. The techniques of 2D Fourier transformation and, for the first time, the triple correlation function are used. Introducing measures for the angular and radial order it is possible to observe a supercritical bifurcation scenario for the decaying order. A chronological sequence of an angular and a radial breakdown of the pattern has been revealed. Possible limits of reproducibility and dependence on the frequency of the applied voltage are estimated.